Diffraction grating device and optical apparatus

ABSTRACT

A diffraction grating device for splitting or coupling light beams permits the divergence of the light beams to be minimized easily. A first light beam is incident on a diffraction grating from the side thereof facing the inside of the device, and a second light beam is incident on the diffraction grating from the side thereof facing air. The diffraction grating transmits the first light beam by diffraction of the minus first order so that it travels in the reverse direction along the optical path of the second light beam before incidence, and transmits the second light beam by diffraction of the zero order. The second light beam, transmitted by diffraction of the zero order, spreads over a certain width of wavelengths, but does not diverge even after diffraction.

This application is based on Japanese Patent Applications Nos.2004-342485, 2004-342504, and 2004-342526 filed on Nov. 26, 2004, thecontents of which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a diffraction grating device designedto diffract light of different wavelengths, and to an optical apparatusthat transmits and receives light of different wavelengths.

2. Description of Related Art

In optical communication, optical transport members such as opticalfibers are used to achieve bi-directional transport of light ofdifferent wavelengths. In an optical apparatus used to transmit andreceive light to perform such optical communication, i.e., in an opticalapparatus that, on one hand, makes light carry signals and thentransmits the light to an optical transport member and that, on theother hand, receives light from the optical transport member and thendetects the signal carried by the light, it is necessary to share asingle optical transport medium to handle both the transmitted andreceived light but to arrange in different positions a light emitter fortransmitting light and a light receiver for receiving light. To achievethis, a splitting/coupling member for splitting and coupling light beamsis arranged on an extension line from the optical transport member sothat the optical path from the light emitter to the splitting/couplingmember and the optical path from the splitting/coupling member to thelight receiver are split from each other while the optical paths ofthose two light beams are coupled together (i.e., made coincident witheach other) between the splitting/coupling member and the opticaltransport member.

To increase communication traffic, an optical transport member is oftenmade to transport light of different wavelengths in the same direction.An optical apparatus of this type is provided with a plurality of lightemitters or light receivers, and is further provided with either aplurality of splitting/coupling members or a single splitting/couplingmember that has the capability of splitting light of differentwavelengths fed from an optical transport member.

A splitting/coupling member is typically realized by the use of amultiple-layer film that reflects or transmits incident light accordingto wavelength. A multiple-layer film, however, has the disadvantages ofrequiring a complicated and time-consuming process for the productionthereof and being expensive.

The splitting and coupling of light beams needs to be performed not onlyin an optical apparatus for optical communication but also in an opticalrecording/reproducing apparatus that uses light to achieve the recordingand reading of information to and from a recording medium. JapanesePatent Application Laid-Open No. 2000-163791 proposes the use, as asplitting/coupling member, of a diffraction grating that diffractsincident light at different angles according to wavelength in theoptical head of an optical recording/reproducing apparatus that useslight of different wavelengths.

A diffraction grating consists simply of elevations and depressionsarranged periodically, and can therefore be produced by resin molding.Accordingly, a diffraction grating device provided with a diffractiongrating has the advantage of being suitable for mass production andbeing inexpensive.

By exploiting the wavelength dependence of the diffraction angle offeredby a diffraction grating, it is possible to spatially split a pluralityof light beams having different wavelengths. To achieve significantsplitting, however, the diffraction grating needs to have the elevationsand depressions thereof formed with a small period. Moreover, since thelight that is made incident on the diffraction grating to be diffractedthereby is spread within a certain width of wavelengths, even when aparallel light beam is made incident on the diffraction grating, thediffracted light beam inevitably becomes divergent. The divergence ofthe diffracted light beam is greater the wider the wavelength band ofthe incident light and the smaller the period of the diffractiongrating.

In an apparatus for optical communication, if the diffracted light beamis divergent, part of the light to be transmitted may fail to enter theoptical transport member, or part of the light emerging from the opticaltransport member may fail to enter the light receiver. This results inlower correctness in the signals transmitted and received. To preventthis, optical members for condensing light need to be arranged betweenthe optical transport member and the splitting/coupling member andbetween the splitting/coupling member and the light receiver. This,however, has the disadvantage of making the apparatus larger.

In an optical recording/reproducing apparatus, if the diffracted lightbeam is divergent, the light cannot be converged in a very small area ona recording medium, resulting in a lower recording density, or part ofthe light reflected from the recording medium may fail to enter thelight receiver, resulting in lower reading accuracy. To prevent this,the movable objective lens that is arranged between thesplitting/coupling member and the recording medium needs to be madelarger. This, however, has the disadvantages of making the apparatuslarger and lowering the response speed of the objective lens and thusthe processing speed of the apparatus.

The diffraction efficiency of a diffraction grating tends to be lowerthe smaller the period of the elevations and depressions thereof. Oneway of maintaining high diffraction efficiency while making the periodof the elevations and depressions small is to adopt a Littrowarrangement, an arrangement in which the diffracted light beam is closerto the incident light beam than the normal to the diffraction grating atthe incidence position. However, in an optical apparatus for opticalcommunication, adopting the Littrow arrangement requires the opticaltransport member and the light receiver to be arranged spatially closetogether, making their arrangement difficult.

Moreover, making the period of the elevations and depressions of adiffraction grating smaller results in a greater difference between thediffraction efficiency for the polarization component that isp-polarized with respect to the diffraction grating and the diffractionefficiency for the polarization component that is s-polarized. Inoptical communication, it is customary to use linearly polarized lightto transport signals, and therefore failing to take into considerationthe polarization direction of light with respect to a diffractiongrating results in lower intensity of the transmitted and receivedlight, leading to lower correctness in the signals transmitted andreceived.

SUMMARY OF THE INVENTION

An object of the present invention is to solve the various problemsdescribed above that are experienced with a diffraction grating devicethat is designed to diffract light of different wavelengths. Morespecifically, a first object of the present invention is to provide adiffraction grating device for splitting or coupling light beams thatpermits the divergence of the light beams to be minimized easily, toprovide a diffraction grating device that offers high diffractionefficiency while simultaneously offering a great angle differencebetween the incident and diffracted light beams, and to provide adiffraction grating device that offers high diffraction efficiencyregardless of the polarization direction of the incident light.

Another object of the present invention is to provide a high-performanceoptical apparatus that splits or couples a plurality of light beamshaving different wavelengths. More specifically, a second object of thepresent invention is to provide an optical apparatus that can minimizethe loss of light, to provide an optical apparatus that permits easyarrangement of a component for supplying a light beam and a componentfor receiving the light beam, and to provide an optical apparatus thatcan minimize the lowering of the intensity of light.

To achieve the above objects, in one aspect of the present invention, ina diffraction grating device on which a first light beam having a firstwavelength and a second light beam having a second wavelength longerthan the first wavelength are made incident from different directionsand that makes the first light beam emerge therefrom in the directionfrom which the second light beam is incident, the followingrelationships are fulfilled:n2≧n1·sin θ;Λ/λL≦1/(n1+n1·sin θ); andΛ/λS>1/(n1+n1·sin θ)−0.04,where

-   -   n1 represents the refractive index of the first medium present        on that side of the diffraction grating on which the first light        beam is incident;    -   n2 represents the refractive index of the second medium present        on that side of the diffraction grating opposite to the side        thereof on which the first light beam is incident;    -   Λ represents the period of the elevations and depressions on the        diffraction grating;    -   λS represents the wavelength of the first light beam;    -   λL represents the wavelength of the second light beam; and    -   θ represents the incidence angle at which the first light beam        is incident on the diffraction grating.

This diffraction grating device transmits, by diffraction, the firstlight beam having wavelength λS, and transmits, without diffraction, thesecond light beam having wavelength λL. Thus, this diffraction gratingdevice does not introduce divergence into the second light beam.

To achieve the above objects, in another aspect of the presentinvention, in a diffraction grating device on which a first light beamhaving a first wavelength and a second light beam having a secondwavelength longer than the first wavelength are made incident fromdifferent directions and that makes the first light beam emergetherefrom in the direction from which the second light beam is incident,the following relationships are fulfilled:n2<n1·sin θ;Λ/L≦1/(n1+n1·sin θ); and1/(n1+n1·sin θ)≦Λ/λS≦1/(n2+n1·sin θ),where

-   -   n1 represents the refractive index of the first medium present        on that side of the diffraction grating on which the first light        beam is incident;    -   n2 represents the refractive index of the second medium present        on that side of the diffraction grating opposite to the side        thereof on which the first light beam is incident;    -   Λ represents the period of the elevations and depressions on the        diffraction grating;    -   λS represents the wavelength of the first light beam;    -   λL represents the wavelength of the second light beam; and    -   θ represents the incidence angle at which the first light beam        is incident on the diffraction grating.

This diffraction grating device reflects, by diffraction, the firstlight beam having wavelength λS, and reflects, without diffraction, thesecond light beam having wavelength λL. Thus, this diffraction gratingdevice does not introduce divergence into the second light beam.

To achieve the above objects, in another aspect of the presentinvention, in a diffraction grating device on which a first light beamhaving a first wavelength and a second light beam having a secondwavelength longer than the first wavelength are made incident fromdifferent directions and that makes the first light beam emergetherefrom in the direction from which the second light beam is incident,the following relationships are fulfilled:n2<n1·sin θ;1/(n1+n1·sin θ)≦Λ/λL≦1/(n2+n1·sin θ); and1/ (n2+n1·sin θ)≦Λ/λS≦2/(n1+n1·sin θ),where

-   -   n1 represents the refractive index of the first medium present        on that side of the diffraction grating on which the first light        beam is incident;    -   n2 represents the refractive index of the second medium present        on that side of the diffraction grating opposite to the side        thereof on which the first light beam is incident;    -   Λ represents the period of the elevations and depressions on the        diffraction grating;    -   λS represents the wavelength of the first light beam;    -   λL represents the wavelength of the second light beam; and    -   θ represents the incidence angle at which the first light beam        is incident on the diffraction grating.

This diffraction grating device reflects, by diffraction, the secondlight beam having wavelength λL, and reflects, without diffraction, thefirst light beam having wavelength λS. Thus, this diffraction gratingdevice does not introduce divergence into the first light beam.

To achieve the above objects, in another aspect of the presentinvention, in a diffraction grating device on which a first light beamhaving a first wavelength and a second light beam having a secondwavelength longer than the first wavelength are made incident fromdifferent directions, the diffraction grating device making the firstlight beam emerge therefrom in the direction from which the second lightbeam is incident, the following relationships are fulfilled:n2≧n1·sin θ;Λ/λL≦1/(n2+n1·sin θ); and1/(n2+n1·sin θ)−0.04<Λ/λS<1/(n2+n1·sin θ)+0.02,where

-   -   n1 represents the refractive index of the first medium present        on that side of the diffraction grating on which the first light        beam is incident;    -   n2 represents the refractive index of the second medium present        on that side of the diffraction grating opposite to the side        thereof on which the first light beam is incident;    -   Λ represents the period of the elevations and depressions on the        diffraction grating;    -   λS represents the wavelength of the first light beam;    -   λL represents the wavelength of the second light beam; and    -   θ represents the incidence angle at which the first light beam        is incident on the diffraction grating.

This diffraction grating device transmits, without diffraction, thesecond light beam having wavelength λL, and reflects, withoutdiffraction, the first light beam having wavelength λS. Thus, thisdiffraction grating device does not introduce divergence into either ofthe first and second light beams.

In any of the diffraction grating devices described above, there may befurther provided, separate from the surface on which the diffractiongrating is formed, a surface capable of condensing light. This makes itpossible to further reduce the divergence of the light beams, and evento make the light beams convergent.

The diffraction grating may be formed on a curved surface. This makes itpossible to give the diffraction grating an optical power arising fromrefraction, and thus makes it possible to further reduce the divergenceof the light beams after diffraction, and even to make the light beamsconvergent.

In that case, preferably, at a given point on the curved surface onwhich the diffraction grating is formed, the diffraction grating isprojected onto the plane tangent thereto at that point, and the period Λof the elevations and depressions of the diffraction grating as observedon that plane and the incidence angle θ with respect to that plane areso chosen as to fulfill the relationships noted above.

Preferably, the elevations and depressions of the diffraction gratingare given a substantially rectangular sectional shape as observedparallel to the direction of the period of the elevations anddepressions. This makes it easy to design the diffraction grating, andmakes it easy to produce the diffraction grating device by resinmolding.

To achieve the above objects, according to another aspect of the presentinvention, an optical apparatus that splits or couples a plurality oflight beams having different wavelengths is provided with one of thediffraction grating devices described above and uses the diffractiongrating to split or couple the light beams. Thanks to the diffractiongrating device being so designed as to reduce the divergence of thelight beams after diffraction, it is possible to direct the light beamsinto a small area, and thereby to realize a diffraction grating devicethat operates with reduced loss of light.

Here, preferably, there is further provided a mechanism for varying theincidence angle at which a light beam is incident on the diffractiongrating. With this construction, even in a case where the wavelength oflight varies with temperature or the like, by varying the incidenceangle, it is possible to make the diffracted light beam travel in afixed direction.

There may be further provided an optical component that makes the lightbeam having the first wavelength incident on the diffraction grating andthat receives the light beam having the second wavelength emerging fromthe diffraction grating. With this construction, the diffraction gratingdevice requires only a single optical component through which to receivelight of the first wavelength from the outside and through which to emitlight of the second wavelength to the outside. An example of such anoptical component is an optical fiber.

There may be further provided an optical component that condenses alight beam incident on or emerging from the diffraction grating. Withthis construction, it is possible to turn a light beam incident on thediffraction grating into a more closely parallel light beam, and tofurther reduce the divergence of the light beam emerging from thediffraction grating. Thus, it is possible to realize a diffractiongrating device that operates with further reduced loss of light.

To achieve the above objects, according to another aspect of the presentinvention, in a diffraction grating device that diffracts and reflects alight beam in a first band of wavelengths and that diffracts andreflects and thereby separates a plurality of light beams in a pluralityof bands of wavelengths longer than the wavelengths of the first band,the plurality of light beams being incident from the direction in whichthe light beam in the first band of wavelengths is diffracted, theelevations and depressions on the diffraction grating have a firstperiod in a first direction and a second period longer than the firstperiod in a second direction perpendicular to the first direction.Moreover, the following relationships are fulfilled:λ1L<λ1U<λ2L<λ2U<λ3L<λ3U;n2<n1·sin θ;φ≠0;1/[n  1 ⋅ (1 − sin²θ ⋅ sin²φ)^(1/2) + n  1 ⋅ sin   θ ⋅ cos   φ] ≤ Λ/λ  3U < Λ/λ  2L ≤ 1/[(n  2² − n  1² ⋅ sin²θ ⋅ sin²φ)^(1/2) + n  1 ⋅ sin   θ ⋅ cos   φ]; and1/[(n  2² − n  1² ⋅ sin²θ ⋅ sin²φ)^(1/2) + n  1 ⋅ sin   θ ⋅ cos   φ] ≤ Λ/λ  1U < Λ/λ  1L ≤ 2/[n  1 ⋅ (1 − sin²θ ⋅ sin²φ)^(1/2) + n  1 ⋅ sin   θ ⋅ cos   φ],where

-   -   n1 represents the refractive index of the first medium present        on that side of the diffraction grating that faces optical paths        of the light beams;    -   n2 represents the refractive index of the second medium present        on that side of the diffraction grating opposite to the side        thereof facing the optical paths of the light beams;    -   θ represents the incidence angle at which the principal ray of        the light beams is incident on the diffraction grating;    -   φ represents the angle between the plane perpendicular to the        diffraction grating and parallel to the first direction and the        incidence plane of the principal ray of the light beams;    -   Λ represents the first period of the elevations and depressions        on the diffraction grating;    -   λ1L represents the shortest wavelength of the first band of        wavelengths;    -   λ1U represents the longest wavelength of the first band of        wavelengths;    -   λ2L represents the shortest wavelength of, of the plurality of        bands of wavelengths longer than the wavelengths of the first        band, the band of shortest wavelengths;    -   λ2U represents the longest wavelength of, of the plurality of        bands of wavelengths longer than the wavelengths of the first        band, the band of shortest wavelengths;    -   λ3L represents the shortest wavelength of, of the plurality of        bands of wavelengths longer than the wavelengths of the first        band, the band of longest wavelengths; and    -   λ3U represents the longest wavelength of, of the plurality of        bands of wavelengths longer than the wavelengths of the first        band, the band of longest wavelengths.

In this diffraction grating device, the elevations and depressions ofthe diffraction grating have one period in the first direction andanother period in the second direction, making it possible to producediffraction also in the second direction. Thus, all the light beams canbe made incident on the diffraction grating from directions inclinedrelative to the first direction so as to split, also in the seconddirection, the light beams in the plurality of bands of wavelengthslonger than the wavelengths of the first band. This makes greater theangle difference between the incident light beam in the first band ofwavelengths and the diffracted light beams in the plurality of bands ofwavelengths longer than the wavelengths of the first band. In addition,fulfilling the relationships noted above permits the diffraction gratingto reflect, without diffraction, the light beam in the first band ofwavelengths and to reflect, while producing diffraction of the minusfirst order in them, the plurality of light beams in the bands ofwavelengths longer than the wavelengths of the first band. As a result,the diffraction grating and the plurality of light beams in the bands ofwavelengths longer than the wavelengths of the first band fulfill arelationship close to the Littrow arrangement, resulting in higherdiffraction efficiency with those light beams.

To achieve the above objects, according to another aspect of the presentinvention, in a diffraction grating device that separates a plurality oflight beams spread in different wavelength bands and overlapping withone another, the elevations and depressions of the diffraction gratinghave a first period in a first direction and a second period longer thanthe first period in a second direction perpendicular to the firstdirection. Moreover, the diffraction grating diffracts and reflects alight beam incident thereon in the same direction from which the lightbeam is incident with respect to the normal to the diffraction gratingat the position at which the light beam is incident. Here, the anglebetween the plane perpendicular to the diffraction grating and parallelto the first direction and the incidence plane of the principal ray ofthe light beam incident on the diffraction grating is 0.5° or more but15° or less.

This diffraction grating device fulfills a relationship close to theLittrow arrangement with the plurality of light beams spread in thedifferent wavelength bands, resulting in high diffraction efficiency.Moreover, the elevations and depressions of the diffraction grating haveone period in the first direction and another period in the seconddirection, and the light beams are made incident on the diffractiongrating from directions inclined relative to the first direction. Thismakes it possible to split the light beams also in the second direction.This makes greater the angle difference between the incident light beamsand the separated light beams, and makes greater the angle differencesamong the separated light beams.

In any of the diffraction grating devices described above, preferably,the elevations and depressions of the diffraction grating are given asubstantially rectangular sectional shape as observed parallel to thedirection of the period of the elevations and depressions. This makes iteasy to design the diffraction grating, and makes it easy to produce thediffraction grating device by resin molding.

To achieve the above objects, according to another aspect of the presentinvention, in an optical apparatus provided with a first opticalcomponent that supplies a light beam in a first band of wavelengths anda second optical component that supplies a plurality of light beams indifferent bands of wavelengths longer than the wavelengths of the firstband and that receives the light beam in the first band of wavelengthsfrom the first optical component, the optical apparatus is furtherprovided with the former diffraction grating devices, and uses thediffraction grating to diffract and reflect and thereby direct the lightbeam from the first optical component to the second optical componentand to diffract and reflect and thereby separate the plurality of lightbeams from the second optical component.

In this optical apparatus, thanks to the design of the diffractiongrating device, it is possible to efficiently direct the light beam fromthe first optical component to the second optical component, and toefficiently separate the plurality of light beams from the secondoptical component, while permitting the first and second opticalcomponents to be arranged in positions where they do not interfere witheach other.

Here, the second optical component may be an optical fiber. This makesthe diffraction grating device suitable for optical communication.

Advisably, there is further provided an optical component that condensesa light beam incident on or emerging from the diffraction grating. Thismakes it possible to reduce the divergence of the light beams, resultingin higher light use efficiency.

To achieve the above objects, according to another aspect of the presentinvention, in an optical apparatus provided with an optical componentthat supplies a plurality of light beams spread in different wavelengthbands and overlapping with one another, the optical apparatus separatingthe plurality of light beams, the optical apparatus is further providedwith the latter diffraction grating device, and uses the diffractiongrating to separate the plurality of light beams. In this opticalapparatus, thanks to the design of the diffraction grating device, it ispossible to efficiently separate the light beams in the differentwavelength bands, and in addition makes the handling of the separatedlight beams easy.

Here, the component that supplies the plurality of light beams may be anoptical fiber. This makes the diffraction grating device suitable foroptical communication.

Advisably, there is further provided an optical component that condensesa light beam incident on or emerging from the diffraction grating. Thismakes it possible to reduce the divergence of the light beams, resultingin higher light use efficiency.

To achieve the above objects, according to another aspect of the presentinvention, in a diffraction grating device that diffracts and reflects alight beam in a first band of wavelengths and that diffracts andreflects and thereby separates a plurality of light beams in a pluralityof bands of wavelengths longer than the wavelengths of the first band,the plurality of light beams being incident from the direction in whichthe light beam in the first band of wavelengths is diffracted, thefollowing relationships are fulfilled:λ1L<λ1U<λ2L<λ2U<λ3L<λ3U;n2<n1·sin θ;1/(n1+n1·sin θ)≦Λ/λ3U<Λ/λ2L≦1/(n2+n1·sin θ);1/(n2+n1·sin θ)≦Λ/λ1U<Λ/λ1L≦2/(n1+n1·sin θ); andΛ/λ3L<1/(2·n1·sin θ)<Λ/λ2U,where

-   -   n1 represents the refractive index of the first medium present        on that side of the diffraction grating that faces optical        paths;    -   n2 represents the refractive index of the second medium present        on that side of the diffraction grating opposite to the side        thereof facing the optical paths;    -   θ represents the incidence angle at which the principal ray of        the light beams is incident on the diffraction grating;    -   Λ represents the period of the elevations and depressions on the        diffraction grating;    -   λ1L represents the shortest wavelength of the first band of        wavelengths;    -   λ1U represents the longest wavelength of the first band of        wavelengths;    -   λ2L represents the shortest wavelength of, of the plurality of        bands of wavelengths longer than the wavelengths of the first        band, the band of shortest wavelengths;    -   λ2U represents the longest wavelength of, of the plurality of        bands of wavelengths longer than the wavelengths of the first        band, the band of shortest wavelengths;    -   λ3L represents the shortest wavelength of, of the plurality of        bands of wavelengths longer than the wavelengths of the first        band, the band of longest wavelengths; and    -   λ3U represents the longest wavelength of, of the plurality of        bands of wavelengths longer than the wavelengths of the first        band, the band of longest wavelengths.

Fulfilling the relationships noted above, this diffraction gratingdevice offers high diffraction efficiency with all the light beams inthe different wavelength bands, regardless of the polarizationdirections thereof.

Here, advisably, the period is the period that the elevations anddepressions on the diffraction grating have in a first directionsubstantially parallel to the incidence plane of the principal ray ofthe incident light beams, and the elevations and depressions on thediffraction grating have another period in a second directionperpendicular to the first direction. With this construction, the lightbeams can be made incident on the diffraction grating from directionsinclined relative to the first direction so as to produce diffractionalso in the second direction. This makes greater the angle differencesamong the separated light beams.

Preferably, the following relationship is fulfilled:Λ²/λ2L ² ≦Λy ²/λ2L ²<1/{n1²·[1−(sin θ−1.1·λ2L/(n1·Λ))²]}where

-   -   Λy represents the period of the elevations and depressions on        the diffraction grating in the second direction.        Fulfilling this relationship helps reduce unnecessary        diffraction, and helps increase diffraction efficiency.

Preferably, the elevations and depressions of the diffraction gratingare given a substantially rectangular sectional shape as observedparallel to the direction of the period of the elevations anddepressions. This makes it easy to design the diffraction grating, andmakes it easy to produce the diffraction grating device by resinmolding.

To achieve the above objects, according to another aspect of the presentinvention, in an optical apparatus provided with a first opticalcomponent that supplies a light beam in a first band of wavelengths anda second optical component that supplies a plurality of light beams indifferent bands of wavelengths longer than the wavelengths of the firstband and that receives the light beam in the first band of wavelengthsfrom the first optical component, the optical apparatus is provided withone of the diffraction grating devices described above, and uses thediffraction grating to diffract and reflect and thereby direct the lightbeam from the first optical component to the second optical componentand to diffract and reflect and thereby separate the plurality of lightbeams from the second optical component.

In this optical apparatus, thanks to the design of the diffractiongrating device, regardless of the polarization direction of the lightbeams, it is possible to efficiently direct the light beam from thefirst optical component to the second optical component, and toefficiently separate the light beams in the different wavelength bandsfrom the second optical component.

The second optical component may be an optical fiber. This makes thediffraction grating device suitable for optical communication.

There may be further provided an optical component that condenses alight beam incident on or emerging from the diffraction grating. Withthis construction, it is possible to turn the light beams incident onthe diffraction grating into a closely parallel light beam, and toreduce the divergence of the light beams emerging from the diffractiongrating. This makes it possible to direct the light beams into a smallarea, and thereby to realize a diffraction grating device that operateswith reduced loss of light.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram schematically showing the construction of theoptical apparatus of a first embodiment of the invention;

FIG. 2 is a diagram schematically showing the optical path in onepractical example of the diffraction grating used in the opticalapparatus of the first embodiment;

FIG. 3 is a diagram showing the relationship between the variation ofthe parameters of the diffraction grating and the variation of thediffraction efficiency in the optical apparatus of the first embodiment;

FIG. 4 is a diagram schematically showing the optical path in onepractical example of the diffraction grating used in the opticalapparatus of a second embodiment of the invention;

FIG. 5 is a diagram schematically showing the optical path in onepractical example of the diffraction grating used in the opticalapparatus of a third embodiment of the invention;

FIG. 6 is a diagram schematically showing the construction of theoptical apparatus of a fourth embodiment of the invention;

FIG. 7 is a diagram schematically showing the optical path in onepractical example of the diffraction grating used in the opticalapparatus of the fourth embodiment;

FIG. 8 is a diagram schematically showing the optical path in onepractical example of the diffraction grating used in the opticalapparatus of a fifth embodiment of the invention;

FIG. 9 is a diagram showing the relationship between the variation ofthe parameters of the diffraction grating and the variation of thediffraction efficiency in the optical apparatus of the fifth embodiment;

FIG. 10 is a diagram schematically showing the construction of theoptical apparatus of a sixth embodiment of the invention;

FIG. 11 is a diagram schematically showing the construction of theoptical apparatus of a seventh embodiment of the invention;

FIG. 12 is a diagram schematically showing the construction of theoptical apparatus of an eighth embodiment of the invention;

FIGS. 13A and 13B are a side view and a plan view, respectively,schematically showing the diffraction grating device used in the opticalapparatus of a ninth embodiment of the invention;

FIG. 14 is a diagram schematically showing the construction of theoptical apparatus of a tenth embodiment of the invention;

FIG. 15 is a diagram schematically showing the optical path in onepractical example of the diffraction grating used in the opticalapparatus of the tenth embodiment;

FIG. 16 is a plan view schematically showing the diffraction gratingused in the optical apparatus of an eleventh embodiment of theinvention;

FIG. 17 is a perspective view schematically showing the relationshipbetween the diffraction grating and the angles of the light beams in theeleventh embodiment;

FIG. 18 is a diagram schematically showing the optical path in onepractical example of the diffraction grating used in the opticalapparatus of the eleventh embodiment; and

FIG. 19 is a diagram schematically showing the optical path in onepractical example of the diffraction grating used in the opticalapparatus of a twelfth embodiment of the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Hereinafter, embodiments of the present invention will be described withreference to the accompanying drawings.

First Embodiment

FIG. 1 schematically shows the construction of the optical apparatus 1of a first embodiment of the invention. The optical apparatus 1 is atransmitter/receiver apparatus for use in optical communication, andincludes a light emitter 21, a light emission controller 22, an opticalfiber 31, a light receiver 41, a signal detector 42, and a diffractiongrating device 51.

The light emitter 21 emits a light beam LT to be transmitted. The lightemission controller 22 controls the light emission by the light emitter21 so as to make the light beam LT emitted by the light emitter 21 carrya signal to be transmitted. The light emitter 21 includes, though notillustrated, a laser diode and a condenser lens so as to emit a parallellight beam obtained by condensing with the condenser lens the lightemitted by the laser diode.

The optical fiber 31 transmits to the outside the light beam LT,carrying the signal to be transmitted, from the light emitter 21. Theoptical fiber 31 also receives from the outside a light beam LR carryinga signal to be received.

The light receiver 41 receives the light beam LR received by the opticalfiber 31, and outputs a signal that represents the amount of receivedlight. The signal detector 42 detects from the output signal of thelight receiver 41 the signal carried by the light beam LR. The lightbeam LT and the light beam LR are in different wavelength bands that areapart from each other. The wavelength of the light beam LT is shorterthan that of the light beam LR.

The diffraction grating device 51 has a diffraction grating 52 (see FIG.2) formed on the surface thereof so as to direct the light beam LT fromthe light emitter 21 to the optical fiber 31 and to direct the lightbeam LR from the optical fiber 31 to the light receiver 41.

Now, the design of the diffraction grating 52 will be described. Here,it is assumed that the period of the elevations and depressions of thediffraction grating 52 is Λ; that the height difference between theelevations and depressions of the diffraction grating 52 is h; that, ofthe two media between which the diffraction grating 52 is sandwiched,the one present on the side thereof on which the light beam LT isincident has a refractive index of n1 and the other has a refractiveindex of n2; that the incidence angle at which the light beam isincident on the diffraction grating 52 is θ1; the emergence angle atwhich the light beam emerges from the diffraction grating 52 is θ2; thatthe center wavelength of the light beam LT having the shorter wavelengthis λS; and that the center wavelength of the light beam LR having thelonger wavelength is λL.

The diffraction grating 52 fulfills the relationships (A1) to (A3)below.n2≧n1·sin θ  (A1)Λ/λL≦1/(n1+n1·sin θ)   (A2)Λ/λS>1/(n1+n1·sin θ1)   (A3)

Fulfilling these relationships, the diffraction grating 52 transmits, bydiffraction of the minus first order, the light beam LT having theshorter wavelength, and transmits, by diffraction of the zero order, thelight beam LR having the longer wavelength.

FIG. 2 schematically shows the optical path observed in one practicalexample. In this example, the center wavelength of the transmitted lightbeam LT is 1,310 nm, and the center wavelength of the received lightbeam LR is 1,490 nm; the light beam LT is made incident on thediffraction grating 52 from inside the diffraction grating device 51,and the light beam LR is made incident on the diffraction grating 52from the air side thereof. The relevant parameters are listed inTable 1. Here, the incidence plane of the principal rays of the lightbeams LT and LR is parallel to the direction of the period of thediffraction grating 52. TABLE 1 Diffraction Grating 52 Sectional Shape:Rectangular Elevation-Depression Period Λ: 0.69 μm Elevation-DepressionHeight Difference h: 1.39 μm Elevation Width: 0.35 μm Medium RefractiveIndex: 1.5 Light Beam LT Wavelength (λS): 1310 nm Period/Wavelength(Λ/λS): 0.53 Incidence Angle θ1: 60° Emergence Angle θ2: −42.6°S-Polarized Light Transmission Diffraction Efficiency: 0.72 Light BeamLR Wavelength (λL): 1490 nm Period/Wavelength (Λ/λL): 0.46 IncidenceAngle θ1: 60° Emergence Angle θ2: 35.3° P-Polarized LightTransmissivity: 0.87 S-Polarized Light Transmissivity: 0.73 MeanTransmissivity: 0.8

In Table 1, the elevation width of the diffraction grating 52 denotesthe width of each of the parts thereof that are elevated toward the sideat which the light beam LT is incident (i.e., toward the inside of thediffraction grating device 51). Here, it should be noted that the valueslisted in Table 1 are those observed when, as opposed to in actual usein the optical apparatus 1, the light beams LT and LR are made incidentfrom the same direction so as to be separated from each other. That is,in actual use in the optical apparatus 1, the incidence angle θ1 and theemergence angle θ2 of the light beam LT take the values of each otherlisted in Table 1.

FIG. 3 shows how the diffraction efficiency varies as the value of1/(n1+n1·sin θ1), appearing in formulae (A2) and (A3), varies in thepractical example (n1=1 and θ1=60°) described above. Here, the value of1/(1+1·sin 60°) is 0.536. As will be understood from FIG. 3, thetransmissivity of the light beam LR, which is transmitted by diffractionof the zero order, is increased by setting the center length λL thereofwithin the range defined by formula (A2), and the transmissivity of thelight beam LT, which is transmitted by diffraction of the minus firstorder, is increased by setting the center length λS thereof within therange defined by formula (A3).

Since the divergence of the light beams after diffraction isproportional to the width of the wavelength band thereof, making thediffraction grating 52 transmit, without diffraction, the light beam LRhaving the longer wavelength as is the case with the diffraction gratingdevice 51 used in the optical apparatus 1 of this embodiment iseffective in preventing the divergence of the light beam LR. With thisdesign, the entire light beam LR can be directed to the light receiver41 without making the light receiver 41 large.

Second Embodiment

The optical apparatus 2 of this embodiment, too, is for use in opticalcommunication, and has a construction similar to that of the opticalapparatus 1 shown in FIG. 1. Specifically, the optical apparatus 2includes a light emitter 21, a light emission controller 22, an opticalfiber 31, a light receiver 41, a signal detector 42, and a diffractiongrating device 51.

Now, the design of the diffraction grating 52 formed on the diffractiongrating device 51 in the optical apparatus 2 will be described. Here, asin the first embodiment, it is assumed that the period of the elevationsand depressions of the diffraction grating 52 is Λ; that the heightdifference between the elevations and depressions of the diffractiongrating 52 is h; that, of the two media between which the diffractiongrating 52 is sandwiched, the one present on the side thereof on whichthe light beam LT is incident has a refractive index of n1 and the otherhas a refractive index of n2; that the incidence angle at which thelight beam is incident on the diffraction grating 52 is θ1; theemergence angle at which the light beam emerges from the diffractiongrating 52 is θ2; that the center wavelength of the light beam LT havingthe shorter wavelength is λS; and that the center wavelength of thelight beam LR having the longer wavelength is λL.

The diffraction grating 52 fulfills the relationships (B1) to (B3)below.n2<n1·sin θ(B1)Λ/λL≦1/(n1+n1·sin θ1)   (B2)1/(n1+n1·sin θ1)≦Λ/λS≦1/(n2+n1·sin θ1)   (B3)

Fulfilling these relationships, the diffraction grating 52 reflects, bydiffraction of the minus first order, the light beam LT having theshorter wavelength, and reflects (regularly reflects), by diffraction ofthe zero order, the light beam LR having the longer wavelength.

FIG. 4 schematically shows the optical path observed in one practicalexample. In this example, the center wavelength of the transmitted lightbeam LT is 1,310 nm, and the center wavelength of the received lightbeam LR is 1,490 nm; the light beams LT and LR are made incident on thediffraction grating 52 from inside the diffraction grating device 51.The relevant parameters are listed in Table 2. Here, the incidence planeof the principal rays of the light beams LT and LR is parallel to thedirection of the period of the diffraction grating 52. TABLE 2Diffraction Grating 52 Sectional Shape: Rectangular Elevation-DepressionPeriod Λ: 0.585 μm Elevation-Depression Height Difference h: 0.42 μmElevation Width: 0.293 μm Medium Refractive Index: 1.5 Light Beam LTWavelength (λS): 1310 nm Period/Wavelength (Λ/λS): 0.45 Incidence Angleθ1: 45° Emergence Angle θ2: −51.8° S-Polarized Light TransmissionDiffraction Efficiency: 0.85 Light Beam LR Wavelength (λL): 1490 nmPeriod/Wavelength (Λ/λL): 0.39 Incidence Angle θ1: 45° Emergence Angleθ2: 45° P-Polarized Light Reflectivity: 0.89 S-Polarized LightReflectivity: 0.86 Mean Reflectivity: 0.875

In Table 2, the elevation width of the diffraction grating 52 denotesthe width of each of the parts thereof that are elevated toward the sideat which the light beams LT and LR are incident (i.e., toward the insideof the diffraction grating device 51). Here, it should be noted that thevalues listed in Table 1 are those observed when, as opposed to inactual use in the optical apparatus 2, the light beams LT and LR aremade incident from the same direction so as to be separated from eachother. That is, in actual use in the optical apparatus 2, the incidenceangle θ1 and the emergence angle θ2 of the light beam LT take the valuesof each other listed in Table 2.

The reflectivity of the light beam LR, which is reflected by diffractionof the zero order, is increased by setting the center length λL thereofwithin the range defined by formula (B2), and the reflectivity of thelight beam LT, which is reflected by diffraction of the minus firstorder, is increased by setting the center length λS thereof within therange defined by formula (B3). Here, the value of 1/(1.5+1.5·sin 45°) is0.391, and the value of 1/(1+1.5·sin 45°) is 0.485.

Since the divergence of the light beams after diffraction isproportional to the width of the wavelength band thereof, making thediffraction grating 52 reflect, without diffraction, the light beam LRhaving the longer wavelength as is the case with the diffraction gratingdevice 51 used in the optical apparatus 2 of this embodiment iseffective in preventing the divergence of the light beam LR. With thisdesign, the entire light beam LR can be directed to the light receiver41 without making the light receiver 41 large.

Third Embodiment

The optical apparatus 3 of this embodiment, too, is for use in opticalcommunication, and has a construction similar to that of the opticalapparatus 1 shown in FIG. 1. Specifically, the optical apparatus 3includes a light emitter 21, a light emission controller 22, an opticalfiber 31, a light receiver 41, a signal detector 42, and a diffractiongrating device 51.

Now, the design of the diffraction grating 52 formed on the diffractiongrating device 51 in the optical apparatus 3 will be described. Here, asin the first embodiment, it is assumed that the period of the elevationsand depressions of the diffraction grating 52 is Λ; that the heightdifference between the elevations and depressions of the diffractiongrating 52 is h; that, of the two media between which the diffractiongrating 52 is sandwiched, the one present on the side thereof on whichthe light beam LT is incident has a refractive index of n1 and the otherhas a refractive index of n2; that the incidence angle at which thelight beam is incident on the diffraction grating 52 is θ1; theemergence angle at which the light beam emerges from the diffractiongrating 52 is θ2; that the center wavelength of the light beam LT havingthe shorter wavelength is λS; and that the center wavelength of thelight beam LR having the longer wavelength is λL.

The diffraction grating 52 fulfills the relationships (C1) to (C3)below.n2<n1·sin θ1   (C1)1/(n1+n1·sin θ1)≦Λ/λL≦1/(n2+n1·sin θ1)   (C2)1/(n2+n1·sin θ1)≦Λ/λS≦2/(n1+n1·sin θ1)   (C3)

Fulfilling these relationships, the diffraction grating 52 reflects, bydiffraction of the minus first order, the light beam LR having thelonger wavelength, and reflects (regularly reflects), by diffraction ofthe zero order, the light beam LT having the shorter wavelength.

FIG. 5 schematically shows the optical path observed in one practicalexample. In this example, the center wavelength of the transmitted lightbeam LT is 1,310 nm, and the center wavelength of the received lightbeam LR is 1,490 nm; the light beams LT and LR are made incident on thediffraction grating 52 from inside the diffraction grating device 51.The relevant parameters are listed in Table 3-1. Here, the incidenceplane of the principal rays of the light beams LT and LR is parallel tothe direction of the period of the diffraction grating 52. TABLE 3-1Diffraction Grating 52 Sectional Shape: Rectangular Elevation-DepressionPeriod Λ: 0.6 μm Elevation-Depression Height Difference h: 0.645 μmElevation Width: 0.3 μm Medium Refractive Index: 1.5 Light Beam LTWavelength (λS): 1310 nm Period/Wavelength (Λ/λS): 0.46 Incidence Angleθ1: 60° Emergence Angle θ2: 60° Reflectivity: 0.81 (−1.83 dB) Light BeamLR Wavelength (λL): 1490 nm Period/Wavelength (Λ/λL): 0.40 IncidenceAngle θ1: 60° Emergence Angle θ2: −52.1° P-Polarized Light ReflectionDiffraction Efficiency: 0.83 (−1.63 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.87 (−1.20 dB) Mean Reflection DiffractionEfficiency: 0.85 (−1.41 dB)

In Table 3-1, the elevation width of the diffraction grating 52 denotesthe width of each of the parts thereof that are elevated toward the sideat which the light beams LT and LR are incident (i.e., toward the insideof the diffraction grating device 51). In Table 3-1 are also listed thedB equivalent values of the reflectivity and the reflection efficiency.

The reflectivity of the light beam LR, which is reflected by diffractionof the minus first order, is increased by setting the center length λLthereof within the range defined by formula (C2), and the reflectivityof the light beam LT, which is reflected by diffraction of the zeroorder, is increased by setting the center length λS thereof within therange defined by formula (C3). Here, the value of 1/(1.5+1.5·sin 60°) is0.357, the value of 1/(+1.5·sin 60°) is 0.434, and the value of2/(1.5+1.5·sin 60°) is 0.715.

When the wavelength bands of the light beams LR and LT have the samewidth, the light beam LT having the shorter wavelength diverges lessthan the light beam RT after diffraction. However, even the light beamLT having the shorter wavelength, as the width of the wavelength bandthereof increases, diverges more after diffraction. This makes itdifficult to make the entire light beam LT enter the optical fiber 31.In the diffraction grating device 51 used in the optical apparatus 3 ofthis embodiment, however, the diffraction grating 52 producesdiffraction of the zero order, i.e., no diffraction, in the light beamLT. This prevents the light beam LT from diverging, and makes it easy tomake the entire light beam LT enter the optical fiber 31, of which thediameter is as small as of the order of μm.

The parameters related to the light beam LT as observed when thewavelength band of the light beam LT has a width of ±50 nm aroundwavelength λS are listed in Tables 3-2 and 3-3. The parameters relatedto the light beam LR as observed when the wavelength band of the lightbeam LR has a width of ±10 nm around wavelength λL are listed in Tables3-4 and 3-5. The parameters other than those listed in these tables arethe same as in Table 3-1. TABLE 3-2 Light Beam LT Shortest Wavelength(λS − 50): 1260 nm Period/Wavelength (Λ/(λS − 50)): 0.48 Incidence Angleθ1: 60° Emergence Angle θ2: 60° Reflectivity: 0.85 (−1.43 dB)

TABLE 3-3 Light Beam LT Longest Wavelength (λS + 50): 1360 nmPeriod/Wavelength (Λ/λS + 50)): 0.44 Incidence Angle θ1: 60° EmergenceAngle θ2: 60° Reflectivity: 0.78 (−2.11 dB)

TABLE 3-4 Light Beam LR Shortest Wavelength (λL − 10): 1480 nmPeriod/Wavelength (Λ/(λL − 10)): 0.41 Incidence Angle θ1: 60° EmergenceAngle θ2: −51.1° P-Polarized Light Reflection Diffraction Efficiency:0.82 (−1.76 dB) S-Polarized Light Reflection Diffraction Efficiency:0.81 (−1.80 dB) Mean Reflection Diffraction Efficiency: 0.81 (−1.78 dB)

TABLE 3-5 Light Beam LR Longest Wavelength (λL + 10): 1500 nmPeriod/Wavelength (Λ/(λL + 10)): 0.40 Incidence Angle θ1: 60° EmergenceAngle θ2: −53.2° P-Polarized Light Reflection Diffraction Efficiency:0.83 (−1.62 dB) S-Polarized Light Reflection Diffraction Efficiency:0.91 (−0.79 dB) Mean Reflection Diffraction Efficiency: 0.87 (−1.20 dB)

The diffraction grating 52 does not produce diffraction in the lightbeam LT, and thus does not cause any variation in reflection angle evenat the shortest or longest wavelength of the wavelength band thereof.Moreover, as will be clearly understood from Tables 3-2 and 3-3, highreflectivity is obtained even at the shortest and longest wavelengths.

Fourth Embodiment

FIG. 6 schematically shows the construction of the optical apparatus 4of a fourth embodiment of the invention. This optical apparatus 4, too,is, like the optical apparatuses 1 to 3 of the first to thirdembodiments, a transmitter/receiver apparatus, but, unlike them,receives two light beams LR1 and LR2 in different wavelength bands viaan optical fiber 31. Accordingly, the optical apparatus 4 includes, inaddition to a light emitter 21, a light emission controller 22, anoptical fiber 31, a light receiver 41, a signal detector 42, and adiffraction grating device 51 like those described previously, a lightreceiver 43 and a signal detector 44. Thus, the diffraction gratingdevice 51 receives, as the targets that it diffracts, three light beamsin total, namely the transmitted light beam LT and the received lightbeams LR1 and LR2. Of these light beams, the light beam LT has theshortest wavelength, the light beam LR2 has the longest wavelength, andthe light beam LR1 has the middle wavelength.

Now, the design of the diffraction grating 52 formed on the diffractiongrating device 51 in the optical apparatus 4 will be described. Here, itis assumed that the period of the elevations and depressions of thediffraction grating 52 is Λ; that the height difference between theelevations and depressions of the diffraction grating 52 is h; that, ofthe two media between which the diffraction grating 52 is sandwiched,the one present on the side thereof on which the light beam LT isincident has a refractive index of n1 and the other has a refractiveindex of n2; that the incidence angle at which the light beam isincident on the diffraction grating 52 is θ1; the emergence angle atwhich the light beam emerges from the diffraction grating 52 is θ2; thatthe center wavelength of the light beam LT having the shortestwavelength is λS; that the center wavelength of the light beam LR2having the longest wavelength is λL; and that the center wavelength ofthe light beam LR1 having the middle wavelength is λM.

The diffraction grating 52 fulfills the relationships (D1) to (D3)below.n2<n1·sin θ1   (D1)1/(n1+n1·sin θ1)≦Λ/λL≦1/(n2+n1·sin θ1)   (D2)1/(n1+n1·sin θ1)≦Λ/λM≦1/(n2+n1·sin θ1)   (D2a)1/(n2+n1·sin θ1)≦Λ/λS≦2/(n1+n1·sin θ1)   (D3)

Fulfilling these relationships, the diffraction grating 52 reflects, bydiffraction of the minus first order, the light beam LR2 having thelongest wavelength and the light beam LR1 having the middle wavelength,and reflects (regularly reflects), by diffraction of the zero order, thelight beam LT having the shortest wavelength.

FIG. 7 schematically shows the optical path observed in one practicalexample. In this example, the center wavelength of the transmitted lightbeam LT is 1,310 nm, and the center wavelengths of the received lightbeams LR1 and LR2 are 1,490 nm and 1,555 nm, respectively; the lightbeams LT, LR1, and LR2 are made incident on the diffraction grating 52from inside the diffraction grating device 51. The relevant parametersare listed in Table 4-1. Here, the incidence plane of the principal raysof the light beams LT, LR1, and LR2 is parallel to the direction of theperiod of the diffraction grating 52. TABLE 4-1 Diffraction Grating 52Sectional Shape: Rectangular Elevation-Depression Period Λ: 0.629 μmElevation-Depression Height Difference h: 0.645 μm Elevation Width:0.239 μm Medium Refractive Index: 1.5 Light Beam LT Wavelength (λS):1310 nm Incidence Angle θ1: 51° Emergence Angle θ2: 51° Reflectivity:0.76 (−2.41 dB) Light Beam LR1 Wavelength (λM): 1490 nm Incidence Angleθ1: 51° Emergence Angle θ2: −53.3° P-Polarized Light ReflectionDiffraction Efficiency: 0.95 (−0.44 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.85 (−1.45 dB) Mean Reflection DiffractionEfficiency: 0.90 (−0.93 dB) Light Beam LR2 Wavelength (λM): 1555 nmIncidence Angle θ1: 51° Emergence Angle θ2: −60.6° P-Polarized LightReflection Diffraction Efficiency: 0.76 (−2.34 dB) S-Polarized LightReflection Diffraction Efficiency: 0.75 (−2.45 dB) Mean ReflectionDiffraction Efficiency: 0.76 (−2.39 dB)

In Table 4-1, the elevation width of the diffraction grating 52 denotesthe width of each of the parts thereof that are elevated toward the sideat which the light beams LT, LR1, and LR2 are incident (i.e., toward theinside of the diffraction grating device 51).

The reflectivity of the light beams LR1 and LR2, which are reflected bydiffraction of the minus first order, is increased by setting the centerlengths λM and λL thereof within the ranges defined by formulae (D2a andD2), and the reflectivity of the light beam LT, which is reflected bydiffraction of the zero order, is increased by setting the center lengthλS thereof within the range defined by formula (D3). Here, the value of1/(1.5+1.5·sin 51°) is 0.375, the value of 1/(1+1.5·sin 51°) is 0.462,and the value of 2/(1.5+1.5·sin 51°) is 0.750.

Also in this embodiment, as in the third embodiment, the diffractiongrating 52 produces diffraction of the zero order, i.e., no diffraction,in the light beam LT. This prevents the light beam LT from diverging,and makes it easy to make the entire light beam LT enter the thinoptical fiber 31.

The parameters related to the light beam LT as observed when thewavelength band of the light beam LT has a width of ±50 nm aroundwavelength λS are listed in Tables 4-2 and 4-3. The parameters relatedto the light beam LR1 as observed when the wavelength band of the lightbeam LR1 has a width of ±10 nm around wavelength λM are listed in Tables4-4 and 4-5. The parameters related to the light beam LR2 as observedwhen the wavelength band of the light beam LR2 has a width of ±5 nmaround wavelength λL are listed in Tables 4-6 and 4-7. The parametersother than those listed in these tables are the same as in Table 4-1.TABLE 4-2 Light Beam LT Shortest Wavelength (λS − 50): 1260 nm IncidenceAngle θ1: 51° Emergence Angle θ2: 51° Reflectivity: 0.87 (−1.26 dB)

TABLE 4-3 Light Beam LT Longest Wavelength (λS + 50): 1360 nm IncidenceAngle θ1: 51° Emergence Angle θ2: 51° Reflectivity: 0.74 (−2.64 dB)

TABLE 4-4 Light Beam LR1 Shortest Wavelength (λM − 10): 1480 nmIncidence Angle θ1: 51° Emergence Angle θ2: −52.3° P-Polarized LightReflection Diffraction Efficiency: 0.96 (−0.33 dB) S-Polarized LightReflection Diffraction Efficiency: 0.84 (−1.52 dB) Mean ReflectionDiffraction Efficiency: 0.90 (−0.90 dB)

TABLE 4-5 Light Beam LR1 Longest Wavelength (λM + 10): 1500 nm IncidenceAngle θ1: 51° Emergence Angle θ2: −54.4° P-Polarized Light ReflectionDiffraction Efficiency: 0.93 (−0.60 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.85 (−1.45 dB) Mean Reflection DiffractionEfficiency: 0.89 (−1.02 dB)

TABLE 4-6 Light Beam LR2 Shortest Wavelength (λL − 5): 1550 nm IncidenceAngle θ1: 51° Emergence Angle θ2: −60° P-Polarized Light ReflectionDiffraction Efficiency: 0.78 (−2.12 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.77 (−2.30 dB) Mean Reflection DiffractionEfficiency: 0.78 (−2.21 dB)

TABLE 4-7 Light Beam LR2 Longest Wavelength (λL + 5): 1560 nm IncidenceAngle θ1: 51° Emergence Angle θ2: −61.2° P-Polarized Light ReflectionDiffraction Efficiency: 0.74 (−2.56 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.74 (−2.62 dB) Mean Reflection DiffractionEfficiency: 0.74 (−2.59 dB)

The diffraction grating 52 does not produce diffraction in the lightbeam LT, and thus does not cause any variation in reflection angle evenat the shortest or longest wavelength of the wavelength band thereof.Moreover, as will be clearly understood from Tables 4-2 and 4-3, highreflectivity is obtained even at the shortest and longest wavelengths.

Fifth Embodiment

The optical apparatus 5 of this embodiment, too, is for use in opticalcommunication, and has a construction similar to that of the opticalapparatus 1 shown in FIG. 1. Specifically, the optical apparatus 5includes a light emitter 21, a light emission controller 22, an opticalfiber 31, a light receiver 41, a signal detector 42, and a diffractiongrating device 51.

Now, the design of the diffraction grating 52 formed on the diffractiongrating device 51 in the optical apparatus 5 will be described. Here, asin the first embodiment, it is assumed that the period of the elevationsand depressions of the diffraction grating 52 is Λ; that the heightdifference between the elevations and depressions of the diffractiongrating 52 is h; that, of the two media between which the diffractiongrating 52 is sandwiched, the one present on the side thereof on whichthe light beam LT is incident has a refractive index of n1 and the otherhas a refractive index of n2; that the incidence angle at which thelight beam is incident on the diffraction grating 52 is θ1; theemergence angle at which the light beam emerges from the diffractiongrating 52 is θ2; that the center wavelength of the light beam LT havingthe shorter wavelength is λS; and that the center wavelength of thelight beam LR having the longer wavelength is λL.

The diffraction grating 52 fulfills the relationships (E1) to (E3)below.n2>n1·sin θ1   (E1)Λ/λL≦1/(n2+n1·sin θ1)   (E2)1/(n2+n1·sin θ1)−0.04<Λ/λS<1/(n2+n1·sin θ1)+0.02   (E3)

Fulfilling these relationships, the diffraction grating 52 transmits, bydiffraction of the zero order, the light beam LR having the longerwavelength, and reflects (regularly reflects), by diffraction of thezero order, the light beam LT having the shorter wavelength.

FIG. 8 schematically shows the optical path observed in one practicalexample. In this example, the center wavelength of the transmitted lightbeam LT is 1,310 nm, and the center wavelength of the received lightbeam LR is 1,490 nm; the light beams LT and LR are made incident on thediffraction grating 52 from inside the diffraction grating device 51.The relevant parameters are listed in Table 5-1. Here, the incidenceplane of the principal rays of the light beams LT and LR is parallel tothe direction of the period of the diffraction grating 52. TABLE 5-1Diffraction Grating 52 Sectional Shape: Rectangular Elevation-DepressionPeriod Λ: 0.667 μm Elevation-Depression Height Difference h: 1.167 μmElevation Width: 0.267 μm Medium Refractive Index: 1.5 Light Beam LTWavelength (λS): 1310 nm Period/Wavelength (Λ/λS): 0.509 Incidence Angleθ1: 36° Emergence Angle θ2: 36° Reflectivity: 0.71 (−2.93 dB) Light BeamLR Wavelength (λL): 1490 nm Period/Wavelength (Λ/λL): 0.448 IncidenceAngle θ1: 36° Emergence Angle θ2: 61.8° P-Polarized LightTransmissivity: 0.91 (−0.86 dB) S-Polarized Light Transmissivity: 0.76(−2.34 dB) Mean Transmissivity: 0.83 (−1.57 dB)

In Table 5-1, the elevation width of the diffraction grating 52 denotesthe width of each of the parts thereof that are elevated toward the sideat which the light beams LT and LR are incident (i.e., toward the insideof the diffraction grating device 51).

FIG. 9 shows how the diffraction efficiency varies as the value of1/(n2+n1·sin θ1), appearing in formulae (E2) and (E3), varies in thepractical example (n1=1.5, n2=1, and θ1=36°) described above. Here, thevalue of 1/(1+1.5·sin 36°) is 0.531. As will be understood from FIG. 9,the transmissivity of the light beam LR, which is transmitted bydiffraction of the zero order, is increased by setting the center lengthλL thereof within the range defined by formula (E2), and thereflectivity of the light beam LT, which is reflected by diffraction ofthe zero order, is increased by setting the center length λS thereofwithin the range defined by formula (E3).

In the optical apparatus 5, the diffraction grating 52 producesdiffraction of the zero order, i.e., no diffraction, in both the lightbeams LT and LR. This prevents the light beams LT and LR from diverging,and makes it easy to make the entire light beam LT enter the thinoptical fiber 31 and to make the entire light beam LR enter the smalllight receiver 41.

The parameters related to the light beam LT as observed when thewavelength band of the light beam LT has a width of ±50 nm aroundwavelength λS are listed in Tables 5-2 and 5-3. The parameters relatedto the light beam LR as observed when the wavelength band of the lightbeam LR has a width of ±10 nm around wavelength λL are listed in Tables5-4 and 5-5. The parameters other than those listed in these tables arethe same as in Table 5-1. TABLE 5-2 Light Beam LT Shortest Wavelength(λS − 50): 1260 nm Period/Wavelength (Λ/(λS − 50)): 0.529 IncidenceAngle θ1: 36° Emergence Angle θ2: 36° Reflectivity: 0.85 (−1.39 dB)

TABLE 5-3 Light Beam LT Longest Wavelength (λS + 50): 1360 nmPeriod/Wavelength (Λ/(λS + 50)): 0.490 Incidence Angle θ1: 36° EmergenceAngle θ2: 36° Reflectivity: 0.59 (−4.65 dB)

TABLE 5-4 Light Beam LR Shortest Wavelength (λL − 10): 1480 nmPeriod/Wavelength (Λ/(λL − 10)): 0.451 Incidence Angle θ1: 36° EmergenceAngle θ2: 61.8° P-Polarized Light Transmissivity: 0.90 (−0.92 dB)S-Polarized Light Transmissivity: 0.76 (−2.44 dB) Mean Transmissivity:0.83 (−1.64 dB)

TABLE 5-5 Light Beam LR Longest Wavelength (λL + 10): 1500 nmPeriod/Wavelength (Λ/(λL + 10)): 0.445 Incidence Angle θ1: 36° EmergenceAngle θ2: 61.8° P-Polarized Light Transmissivity: 0.91 (−0.80 dB)S-Polarized Light Transmissivity: 0.77 (−2.25 dB) Mean Transmissivity:0.84 (−1.50 dB)

The diffraction grating 52 does not produce diffraction in the lightbeams LT and LR, and thus does not cause any variation in emergenceangle even at the shortest or longest wavelength of the wavelength bandsthereof. Moreover, high reflectivity or transmissivity is obtained evenat the shortest and longest wavelengths of those wavelength bands.

Sixth Embodiment

FIG. 10 schematically shows the construction of the optical apparatus 6of a sixth embodiment of the invention. This optical apparatus 6, too,is, like the optical apparatus 5 of the fifth embodiment, atransmitter/receiver apparatus, but, unlike it, transmits two lightbeams LT1 and LT2 in different wavelength bands via an optical fiber 31.Accordingly, the optical apparatus 6 includes, in addition to a lightemitter 21, a light emission controller 22, an optical fiber 31, a lightreceiver 41, a signal detector 42, and a diffraction grating device 51like those described previously, a light emitter 23 and a light emissioncontroller 24. Thus, the diffraction grating device 51 receives, as thetargets that it diffracts, three light beams in total, namely thetransmitted light beams LT1 and LT2 and the received light beam LR. Ofthese light beams, the light beam LT1 has the shortest wavelength, thelight beam LR has the longest wavelength, and the light beam LT2 has themiddle wavelength.

Now, the design of the diffraction grating 52 formed on the diffractiongrating device 51 in the optical apparatus 6 will be described. Here, itis assumed that the period of the elevations and depressions of thediffraction grating 52 is Λ; that the height difference between theelevations and depressions of the diffraction grating 52 is h; that, ofthe two media between which the diffraction grating 52 is sandwiched,the one present on the side thereof on which the light beam LT isincident has a refractive index of n1 and the other has a refractiveindex of n2; that the incidence angle at which the light beam isincident on the diffraction grating 52 is θ1; the emergence angle atwhich the light beam emerges from the diffraction grating 52 is θ2; thatthe center wavelength of the light beam LT1 having the shortestwavelength is λS; that the center wavelength of the light beam LR havingthe longest wavelength is λL; and that the center wavelength of thelight beam LT2 having the middle wavelength is λM.

The diffraction grating 52 fulfills the relationships (F1) to (F4)below.n2≧n1·sin θ1   (F1)Λ/λL≦1/(n2+n1·sin θ1)   (F2)1/(n2+n1·sin θ1)−0.04<Λ/λM<1/(n2+n1·sin θ1)+0.02   (F3)Λ/λS≧1/(n2+n1·sin θ1)   (F4)

With this design, the diffraction grating 52 transmits, by diffractionof the zero order, the light beam LR having the longest wavelength andthe light beam LT1 having the shortest wavelength, and reflects(regularly reflects), by diffraction of the zero order, the light beamLT2 having the middle wavelength.

Seventh Embodiment

The optical apparatus 7 of this embodiment is a modified version of theoptical apparatus 4 of the fourth embodiment, which receives two lightbeams LR1 and LR2 in different wavelength bands via an optical fiber 31.FIG. 11 shows the diffraction grating device 51 used in the opticalapparatus 7 and the optical path of the light beams LR1 and LR2. Of thesurface of the diffraction grating device 51 other than where thediffraction grating 52 is formed, the part 53 through which the lightbeams LR1 and LR2 pass after diffraction is formed into a curved surfacein the shape of a cylinder of which the center line is perpendicular tothe direction of the period of the diffraction grating 52. Thus, thispart 53 acts as a convex lens with respect to the light beams LR1 andLR2.

Since the light beams LR1 and LR2 are diffracted light, they divergeaccording to the width of the wavelength bands thereof. By giving alight-condensing function to the part 53 through which they pass in thisway, however, it is possible to turn the light beams LR1 and LR2 intoclosely parallel or even converging light beams. This makes it possibleto make the entire light beams LR1 and LR2 enter the light receivers 41and 42 without making the light receivers 41 and 42 large. Moreover, bygiving the part 53 an appropriately curved shape, it is possible toreduce aberrations.

If the radius of curvature of the part 53, which has a curved surface,is made equal to the distance from the point at which the light beamsare incident on the diffraction grating 52 to the part 53, then the part53 do not have a light-condensing function. Even then, it is possible toprevent the light beams LR1 and LR2 from further diverging as a resultof refraction as is the case if the part 53 has a flat surface.

In this embodiment, it is assumed that the center wavelength λM of thelight beam LR1 is 1,480 nm; that the center wavelength λL of the lightbeam LR2 is 1,500 nm; that the incidence angle θ1 of the light beams LR1and LR2 is 51°; that the reflection angle θ2 of the light beam LR1 is52.3°; and that the reflection angle θ2 of the light beam LR2 is 54.3°.Though not illustrated, the incidence angle of the transmitted lightbeam LT is 55.4° when the center wavelength λS thereof is 1,260 nm,51.8° when the center wavelength λS thereof is 1,310 nm, and 48.39° whenthe center wavelength λS thereof is 1,360 nm.

Eighth Embodiment

The optical apparatus 8 of this embodiment is a modified version of theoptical apparatus 2 of the second embodiment, which reflects, bydiffraction of the minus first order, the transmitted light beam LT.FIG. 12 shows the diffraction grating device 51 used in the opticalapparatus 8 and the optical path of the light beam LT. Of the surface ofthe diffraction grating device 51 elsewhere than where the diffractiongrating 52 is formed, the part 54 through which the light beam LT passesbefore incidence is formed into a curved surface in the shape of acylinder of which the center line is perpendicular to the direction ofthe period of the diffraction grating 52. Thus, this part 54 acts as aconvex lens with respect to the light beam LT. Even in a case where thelight beam LT from the light emitter 21 is divergent, by giving alight-condensing function to the part 54 in this way, it is possible toturn the light beam LT incident on the diffraction grating 52 into aclosely parallel light beam.

The optical apparatus 8 further includes an arc-shaped rail 25. Thisrail 25 runs about the point at which the light beam LT is incident onthe diffraction grating 52, and is laid on the plane perpendicular tothe diffraction grating 52 and parallel to the direction of the periodthereof. The light emitter 21 is movable along the rail 25 so that, asthe light emitter 21 moves, the incidence angle at which the light beamLT is incident on the diffraction grating 52 varies. Moreover, the lightemitter 21 is fitted with a temperature sensor 26 so that the positionof the light emitter 21 is controlled according to the temperaturedetected by the temperature sensor 26.

The characteristics of the laser diode provided in the light emitter 21that emits the light beam LT vary with temperature, and accordingly thewavelength of the light beam LT varies with temperature. As thewavelength varies, the diffraction angle at which the light beam LT isdiffracted by the diffraction grating 52 varies, possibly causing partof the diffracted light beam LT to fail to enter the optical fiber 31.However, by varying the incidence angle of the light beam LT withrespect to the diffraction grating 52 according to temperature in thisway, it is possible to ensure that the entire light beam LT enters theoptical fiber 31.

Instead of providing the temperature sensor 26, it is also possible toprovide a plurality of optical sensors 35 near the end of the opticalfiber 31 so that the position of the light emitter 21 is controlledaccording to which of the optical sensors 35 the light beam LT enters.In this case, by controlling the position of the light emitter 21 insuch a way that the light beam LT enters none of the optical sensors 35,it is possible to make the entire light beam LT enter the optical fiber31.

Here, the wavelengths of the light beams LT and LR, the design of thediffraction grating 52, and other relevant parameters are the same as inthe second embodiment.

Ninth Embodiment

FIGS. 13A and 13B show the diffraction grating device 51 used in theoptical apparatus 9 of this embodiment. FIG. 13A is a side view, andFIG. 13B is a plan view. In this embodiment, the surface of thediffraction grating device 51 is formed into a convex curved surface,and a diffraction grating 52 is formed on this curved surface. Formingthe diffraction grating 52 on a curved surface permits the diffractiongrating 52 to have an optical power resulting from refraction. Thismakes it possible to reduce the divergence of the emergent light beam,thereby eliminating the need to separately provide a means for reducingthe divergence of the light beam after emergence.

In a case where the light beam incident on the diffraction grating 52 isnot a parallel light beam, by making the intervals between theelevations and depressions of the diffraction grating 52 vary graduallyinstead of making them constant, or by forming the individual elevationsand depressions in curved lines instead of forming them in straightlines, it is possible to reduce aberrations that cause the divergence ofthe light beam.

In a case where a diffraction grating 52 is formed on a curved surfaceas in this embodiment, at a given point on the diffraction grating 52,the diffraction grating 52 is projected onto the plane P tangent theretoat that point, and the incidence angle θ1 with respect to the plane Pand the period Λ as observed on the plane P are so chosen as to fulfillthe relationships expressed by one of the groups of formulae (A1) to(A3), (B1) to (B3), (C1) to (C3), (D1) to (D3), (E1) to (E3), and (F1)to (F4). This makes it possible to obtain the same effects as obtainedin the corresponding embodiment described previously.

Tenth Embodiment

FIG. 14 schematically shows the construction of the optical apparatus 10of a tenth embodiment. The optical apparatus 10 is an opticalrecording/reproducing apparatus that records and reads information toand from a recording medium by using light. The optical apparatus 10includes three light emitters 27, 28, and 29, two diffraction gratingdevices 55 and 57, and an objective lens 61. The diffraction gratingdevices 55 and 57 are both prism-shaped, and each have a diffractiongrating 56 or 58, respectively (see FIG. 15), formed on one surfacethereof.

The light emitters 27, 28, and 29 emit light beams LT1, LT2, and LT3,respectively, in different wavelength bands so that a recording medium Mis irradiated with those light beams. The light emitters 27, 28, and 29each include, though not illustrated, a laser diode and a condenser lensso as to emit a parallel light beam obtained by condensing with thecondenser lens the light emitted by the laser diode.

The diffraction grating device 55 couples together the light beam LT1from the light emitter 27 and the light beam LT2 from the light emitter28. On the other hand, the diffraction grating device 57 couplestogether the light beams LT1 and LT2 as coupled together by thediffraction grating device 55 and the light beam LT3 from the lightemitter 29.

The objective lens 61 makes the light beams LT1, LT2, and LT3 as coupledtogether by the diffraction grating device 55 converge on the recordingmedium M.

Now, the design of the diffraction gratings 56 and 58 formed on thediffraction grating devices 55 and 57 will be described. Here, it isassumed that the period of the elevations and depressions of thediffraction grating 56 or 58 is Λ; that the height difference betweenthe elevations and depressions of the diffraction grating 56 or 58 is h;that, of the two media between which the diffraction grating 56 or 58 issandwiched, the one present on the side thereof on which the light beamis incident has a refractive index of n1 and the other has a refractiveindex of n2; that the incidence angle at which the light beam isincident on the diffraction grating 56 or 58 is θ1; the emergence angleat which the light beam emerges from the diffraction grating 56 or 58 isθ2; and that, of the wavelength bands in which the light beams LT1, LT2,and LT3 lie, the one covering the shortest wavelengths has a centerwavelength of λS, the one covering the longest wavelengths has a centerwavelength of λL, and the one covering the middle wavelengths has acenter wavelength of λM. Here, it should be noted that, although theparameters of the diffraction grating 56 and those of the diffractiongrating 58 are represented by common symbols, the diffraction gratings56 and 58 have different values for each parameter (for example, theperiod Λ).

The diffraction gratings 56 and 58 each fulfill the relationships (G1)to (G4) below.n2>n1·sin θ1   (G1)Λ/λL≦1/(n2+n1·sin θ1)   (G2)Λ/λM≈1/(n2+n1·sin θ1)   (G3)Λ/λS≧1/(n2+n1·sin θ1)   (G4)

Fulfilling these relationships, the diffraction gratings 56 and 58transmit or reflect the light beams LT1, LT2, and LT3 while producingdiffraction of the zero order, i.e., no diffraction, in any of them.

FIG. 15 schematically shows the optical path observed in one practicalexample. In this example, the center wavelengths of the wavelength bandsof the light beams LT1, LT2, and LT3 are 650 nm, 780 nm, and 405 nm,respectively; the light beam LT1 is made incident on the diffractiongrating 56 from inside the diffraction grating device 55, and the lightbeam LT2 is made incident on the diffraction grating 56 from the airside of the diffraction grating device 55; the light beams LT1 and LT2are made incident on the diffraction grating 58 from the air side of thediffraction grating device 57, and the light beam LT3 is made incidenton the diffraction grating 58 from inside the diffraction grating device57. The relevant parameters are listed in Tables 6-1 and 6-2. In thisexample, the center wavelength of the light beam LT3 equals the shortestwavelength λS, the center wavelength of the light beam LT2 equals thelongest wavelength λL, and the center wavelength of the light beam LT1equals the middle wavelength λM.

With respect to the diffraction gratings 56 and 58, the light beam LT1is s-polarized, the light beam LT2 is p-polarized, and the light beamLT3 is s-polarized. In FIG. 15, a double-headed arrow on the opticalpath indicates that the polarization direction is parallel to the planeof the drawing, and a double circle on the optical path indicates thatthe polarization direction is perpendicular to the plane of the drawing.TABLE 6-1 Diffraction Grating 56 Sectional Shape: RectangularElevation-Depression Period Λ: 326 nm Elevation-Depression HeightDifference h: 571 nm Elevation Width: 163 nm Medium Refractive Index:1.5 Light Beam LT1 Wavelength (λM): 650 nm Period/Wavelength (Λ/λM):0.502 Incidence Angle θ1: 38° Emergence Angle θ2: 38° S-Polarized LightReflectivity: 0.962 Light Beam LT2 Wavelength (λL): 780 nmPeriod/Wavelength (Λ/λL): 0.418 Incidence Angle θ1: 67.4° EmergenceAngle θ2: 38° P-Polarized Light Transmissivity: 0.952

TABLE 6-2 Diffraction Grating 58 Sectional Shape: RectangularElevation-Depression Period Λ: 203 nm Elevation-Depression HeightDifference h: 571 nm Elevation Width: 163 nm Medium Refractive Index:1.5 Light Beam LT1 Wavelength (λM): 650 nm Period/Wavelength (Λ/λM):0.312 Incidence Angle θ1: 67.4° Emergence Angle θ2: 38° S-PolarizedLight Transmissivity: 0.74 Light Beam LT2 Wavelength (λL): 780 nmPeriod/Wavelength (Λ/λL): 0.260 Incidence Angle θ1: 67.4° EmergenceAngle θ2: 38° P-Polarized Light Transmissivity: 0.944 Light Beam LT3Wavelength (λS): 405 nm Period/Wavelength (Λ/λS): 0.501 Incidence Angleθ1: 38° Emergence Angle θ2: 38° S-Polarized Light Reflectivity: 0.962

In Tables 6-1 and 6-2, the elevation width of the diffraction grating 56or 58 denotes the width of each of the parts thereof that are elevatedtoward the inside of the diffraction grating device 55 or 57. Theincidence angle at which the light beams LT1, LT2, and LT3 are incidenton the surface of the diffraction grating devices 55 and 57 elsewherethan where the diffraction gratings 56 and 58 are formed is 90°.Assuming that the transmissivity through the surface elsewhere thanwhere the diffraction gratings 56 and 58 are formed is 1, the amounts oflight contained in the light beams LT1, LT2, and LT3 after they havepassed through the diffraction grating devices 55 and 57 arerespectively 0.712, 0.899, and 0.962 times the amounts of lightcontained in those light beams before they pass through the diffractiongrating devices 55 and 57. Here, the value of 1/(1.5+sin 38°) is 0.520.

Eleventh Embodiment

The optical apparatus 11 of an eleventh embodiment of the invention is atransmitter/receiver apparatus for use in optical communication. Thisoptical apparatus 11, like the optical apparatus 4 of the fourthembodiment shown in FIG. 6, transmits a light beam LT via an opticalfiber 31, and receives two light beams LR1 and LR2 via the optical fiber31. The light beams LT, LR1, and LR2 are in different wavelength bands.

Here, a diffraction grating 52 is formed on a diffraction grating device51, and the elevations and depressions of the diffraction grating 52have separate periods in a first and a second direction that areperpendicular to each other. FIG. 16 schematically shows the diffractiongrating 52. The periods of the elevations and depressions in the firstand second directions differ from each other, the period in the seconddirection being shorter. In the following description, the period in thefirst direction is referred to as the main period, and the period in thesecond direction is referred to as the sub period. Moreover, here, it isassumed that the main period is Λx and the sub period is Λy; and thatthe distance between the elevations 52 a in the main period direction isWx and the distance between the elevations 52 a in the sub perioddirection is Wy.

FIG. 17 shows the relationship between the diffraction grating 52 andthe angles of the light beams. The angle φ between the planeperpendicular to the diffraction grating 52 and parallel to thedirection of the main period and the incidence plane of the light beamsincident on the diffraction grating 52 is referred to as the directionangle. The incidence angle θ1 is the angle between the principal ray ofthe incident light beams and the normal to the diffraction grating 52 asmeasured in the incidence plane.

In the optical apparatus 11, the light beams LT, LR1, and LR2 are madeincident on the diffraction grating 52 in such a way that the incidenceplanes of those light beams are slightly inclined relative to thedirection of the main period. Thus, the direction angle of none of thelight beams LT, LR1, and LR2 equals 0.

Now, the design of the diffraction grating 52 formed on the diffractiongrating device 51 in the optical apparatus 11 will be described. Here,it is assumed that the main period (Λx) of the elevations anddepressions of the diffraction grating 52 is Λ; that the heightdifference between the elevations and depressions of the diffractiongrating 52 is h; that, of the two media between which the diffractiongrating 52 is sandwiched, the one present on the side thereof on whichthe light beam is incident has a refractive index of n1 and the otherhas a refractive index of n2; that the incidence angle at which thelight beam is incident on the diffraction grating 52 is θ1; theemergence angle at which the light beam emerges from the diffractiongrating 52 is θ2; that, of the wavelength bands in which the light beamsLT, LR1, and LR2 lie, the one covering the shortest wavelengths rangesfrom the shortest wavelength of λ1L to the longest wavelength of λ1U,the one covering the longest wavelengths ranges from the shortestwavelength of λ3L to the longest wavelength of λ3U, and the one coveringthe middle wavelengths ranges from the shortest wavelength of λ2L to thelongest wavelength of λ2U.

The diffraction grating 52 fulfills the relationships (H1) to (H5)below.λ1L<λ1U<λ2L<λ2U<λ3L<λ3U   (H1)n2<n1·sin θ1   (H2)φ≠0   (H3)1/[n1·(1·sin²η1·sin²φ)^(1/2) +n1·sin θ1·cos φ]≦Λ/λ3U<Λ/λ2L≦1/[(n2²⁻n1²·sin²θ1·sin²φ)^(1/2) +n1·sin θ1·cos φ]  (H4)1/[(n2² −n1²·sin²θ1·sin²φ)^(1/2) +n1·sin θ1·cosφ]≦Λ/λ1U<Λ/λ1L≦2/[n1·(1−sin²θ1·sin²φ)^(1/2) +n1·sin θ1·cos φ]  (H5)

Fulfilling these relationships, the diffraction grating 52 reflects(regularly reflects), by diffraction of the zero order, the transmittedlight beam LT, and reflects, by diffraction of the minus first order,the two received light beams LR1 and LR2. The diffraction grating 52 andthe light beams LR1 and LR2 fulfill a relationship close to the Littrowarrangement.

FIG. 18 schematically shows the optical path observed in one practicalexample. In this example, the center wavelength of the transmitted lightbeam LT is 1,310 nm, and the center wavelengths of the received lightbeams LR1 and LR2 are 1,490 nm and 1,555 nm, respectively; the lightbeams LT, LR1, and LR2 are made incident on the diffraction grating 52from inside the diffraction grating device 51. The relevant parametersare listed in Table 7-1. The direction angle φ of the light beams LT,LR1, and LR2 is 10°. TABLE 7-1 Diffraction Grating 52 Sectional Shape:Rectangular Elevation-Depression Main Period Λx (Λ): 0.649 μmElevation-Depression Sub Period Λx: 1.298 μm Elevation-Depression HeightDifference h: 0.649 μm Main-Period-Direction Elevation Width Wx: 0.389μm Sub-Period-Direction Elevation Width Wy: 0.13 μm Medium RefractiveIndex: 1.48 Light Beam LT Wavelength (λS): 1310 nm Period/Wavelength(Λx/λS): 0.495 Direction angle φ: 10° Incidence Angle θ1: 52.5°Emergence Angle θ2: 52.5° Reflectivity: 0.77 (−1.14 dB) Light Beam LR1Wavelength (λM): 1490 nm Period/Wavelength (Λx/λM): 0.436 Directionangle φ: 10° Incidence Angle θ1: 52.5° Emergence Angle θ2: −49.3°P-Polarized Light Reflection Diffraction Efficiency: 0.92 (−0.35 dB)S-Polarized Light Reflection Diffraction Efficiency: 0.95 (−0.22 dB)Mean Reflection Diffraction Efficiency: 0.94 (−0.28 dB) Light Beam LR2Wavelength (λL): 1555 nm Period/Wavelength (Λx/λL): 0.417 Directionangle φ: 10° Incidence Angle θ1: 52.5° Emergence Angle θ2: −55.7°P-Polarized Light Reflection Diffraction Efficiency: 0.82 (−0.85 dB)S-Polarized Light Reflection Diffraction Efficiency: 0.90 (−0.45 dB)Mean Reflection Diffraction Efficiency: 0.86 (−0.64 dB)

In Table 7-1, the elevation width of the diffraction grating 52 denotesthe width of each of the parts thereof that are elevated toward the sideat which the light beams LT, LR1, and LR2 are incident (i.e., toward theinside of the diffraction grating device 51).

The parameters related to the shortest wavelength (λ1L) and the longestwavelength (λ1U) of the light beam LT as observed when the wavelengthband thereof has a width of 100 nm are listed in Tables 7-2 and 7-3. Theparameters related to the shortest wavelength (λ2L) and the longestwavelength (λ2U) of the light beam LR1 as observed when the wavelengthband thereof has a width of 20 nm are listed in Tables 7-4 and 7-5. Theparameters related to the shortest wavelength (λ3L) and the longestwavelength (λ3U) of the light beam LR2 as observed when the wavelengthband thereof has a width of 10 nm are listed in Tables 7-6 and 7-7.TABLE 7-2 Light Beam LT Shortest Wavelength (λ1L): 1260 nmPeriod/Wavelength (Λx/λ1L): 0.515 Direction angle φ: 10° Incidence Angleθ1: 52.5° Emergence Angle θ2: 52.5° Reflectivity: 0.82 (−0.86 dB)

TABLE 7-3 Light Beam LT Longest Wavelength (λ1U): 1360 nmPeriod/Wavelength (Λx/λ1U): 0.477 Direction angle φ: 10° Incidence Angleθ1: 52.5° Emergence Angle θ2: 52.5° Reflectivity: 0.72 (−1.46 dB)

TABLE 7-4 Light Beam LR1 Shortest Wavelength (λ2L): 1480 nmPeriod/Wavelength (Λx/λ2L): 0.438 Direction angle φ: 10° Incidence Angleθ1: 52.5° Emergence Angle θ2: −48.4° P-Polarized Light ReflectionDiffraction Efficiency: 0.91 (−0.40 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.92 (−0.35 dB) Mean Reflection DiffractionEfficiency: 0.92 (−0.37 dB)

TABLE 7-5 Light Beam LR1 Longest Wavelength (λ2U): 1500 nmPeriod/Wavelength (Λx/λ2U): 0.433 Direction angle φ: 10° Incidence Angleθ1: 52.5° Emergence Angle θ2: −50.2° P-Polarized Light ReflectionDiffraction Efficiency: 0.93 (−0.34 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.96 (−0.16 dB) Mean Reflection DiffractionEfficiency: 0.95 (−0.25 dB)

TABLE 7-6 Light Beam LR2 Shortest Wavelength (λ3L): 1550 nmPeriod/Wavelength (Λx/λ3L): 0.419 Direction angle φ: 10° Incidence Angleθ1: 52.5° Emergence Angle θ2: −55.1° P-Polarized Light ReflectionDiffraction Efficiency: 0.84 (−0.77 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.92 (−0.38 dB) Mean Reflection DiffractionEfficiency: 0.88 (−0.57 dB)

TABLE 7-7 Light Beam LR2 Longest Wavelength (λ3U): 1560 nmPeriod/Wavelength (Λx/λ3U): 0.416 Direction angle φ: 10° Incidence Angleθ1: 52.5° Emergence Angle θ2: −56.2° P-Polarized Light ReflectionDiffraction Efficiency: 0.81 (−0.94 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.89 (−0.52 dB) Mean Reflection DiffractionEfficiency: 0.85 (−0.72 dB)

The values of the lower and upper limits of formula (H4), i.e., thevalues of the following two formulae equal 0.381 and 0.468,respectively, and the values of the periods of the light beams LR1 andLR2 divided by the wavelengths thereof fulfill formula (H4).1/[n1·(1—sin²θ1·sin²φ)^(1/2) +n1·sin θ1·cos φ]1/[(n2² n1²·sin²θ1·sin²φ)^(1/2) +n1·sin θ1·cos φ]

Moreover, the values of the lower and upper limits of formula (H5),i.e., the values of the following two formulae equal 0.468 and 0.763,respectively, and the value of the period of the light beam LT dividedby the wavelength thereof fulfills formula (H5).1/[(n2² −n1²·sin²θ1·sin²φ)^(1/2) +n1·sin θ1·cos φ]2/[n1·(1−sin²θ1·sin²φ)^(1/2) +n1·sin θ1·cos φ]

Fulfilling formula (H4) results in higher diffraction efficiency withthe light beams LR1 and LR2 having the longer wavelengths that arereflected by diffraction of the minus first order. On the other hand,fulfilling formula (H5) results in higher reflection efficiency with thelight beam LT having the shorter wavelength that is regularly reflectedwithout diffraction.

In the optical apparatus of this embodiment, the diffraction grating 52and the light beams LR1 and LR2 fulfill a relationship close to theLittrow arrangement. Nevertheless, since the direction angle φ is not 0,it is possible to alleviate the interference between the optical fiber31 and the light receivers 41 and 43 (see FIG. 6), and this makes iteasy to design the optical apparatus as a whole. However, if thedirection angle φ is in the range from 0° to 0.5°, interference betweenthe optical fiber 31 and the light receivers 41 and 43 is more likely.On the other hand, if the direction angle φ is more than 15°, an undulylarge amount of light is diffracted at unnecessary orders. Thus, it ispreferable that the direction angle φ be 0.5° or more but 15° or less.

For comparison, the parameters as observed when the direction angles φof the light beams LT, LR1, and LR2 equal 0° are listed in Tables 8-1 to8-7. TABLE 8-1 Diffraction Grating Sectional Shape: RectangularElevation-Depression Main Period Λx (Λ): 0.649 μm Elevation-DepressionSub Period Λx: 1.298 μm Elevation-Depression Height Difference h: 0.649μm Main-Period-Direction Elevation Width Wx: 0.389 μmSub-Period-Direction Elevation Width Wy: 0.13 μm Medium RefractiveIndex: 1.48 Light Beam LT Wavelength (λS): 1310 nm Period/Wavelength(Λx/λS): 0.495 Direction angle φ: 0° Incidence Angle θ1: 52.5° EmergenceAngle θ2: 52.5° Reflectivity: 0.81 (−0.90 dB) Light Beam LR1 Wavelength(λM): 1490 nm Period/Wavelength (Λx/λM): 0.436 Direction angle φ: 0°Incidence Angle θ1: 52.5° Emergence Angle θ2: −49.3° P-Polarized LightReflection Diffraction Efficiency: 0.88 (−0.55 dB) S-Polarized LightReflection Diffraction Efficiency: 0.85 (−0.71 dB) Mean ReflectionDiffraction Efficiency: 0.86 (−0.63 dB) Light Beam LR2 Wavelength (λL):1555 nm Period/Wavelength (Λx/λL): 0.417 Direction angle φ: 0° IncidenceAngle θ1: 52.5° Emergence Angle θ2: −55.7° P-Polarized Light ReflectionDiffraction Efficiency: 0.87 (−0.59 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.95 (−0.23 dB) Mean Reflection DiffractionEfficiency: 0.91 (−0.41 dB)

TABLE 8-2 Light Beam LT Shortest Wavelength (λ1L): 1260 nmPeriod/Wavelength (Λx/λ1L): 0.515 Direction angle φ: 0° Incidence Angleθ1: 52.5° Emergence Angle θ2: 52.5° Reflectivity: 0.88 (−0.57 dB)

TABLE 8-3 Light Beam LT Longest Wavelength (λ1U): 1360 nmPeriod/Wavelength (Λx/λ1U): 0.477 Direction angle φ: 0° Incidence Angleθ1: 52.5° Emergence Angle θ2: 52.5° Reflectivity: 0.76 (−1.21 dB)

TABLE 8-4 Light Beam LR1 Shortest Wavelength (λ2L): 1480 nmPeriod/Wavelength (Λx/λ2L): 0.438 Direction angle φ: 0° Incidence Angleθ1: 52.5° Emergence Angle θ2: −48.4° P-Polarized Light ReflectionDiffraction Efficiency: 0.85 (−0.70 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.79 (−1.00 dB) Mean Reflection DiffractionEfficiency: 0.82 (−0.85 dB)

TABLE 8-5 Light Beam LR1 Longest Wavelength (λ2U): 1500 nmPeriod/Wavelength (Λx/λ2U): 0.433 Direction angle φ: 0° Incidence Angleθ1: 52.5° Emergence Angle θ2: −50.2° P-Polarized Light ReflectionDiffraction Efficiency: 0.90 (−0.45 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.89 (−0.50 dB) Mean Reflection DiffractionEfficiency: 0.90 (−0.48 dB)

TABLE 8-6 Light Beam LR2 Shortest Wavelength (λ3L): 1550 nmPeriod/Wavelength (Λx/λ3L): 0.419 Direction angle φ: 0° Incidence Angleθ1: 52.5° Emergence Angle θ2: −55.1° P-Polarized Light ReflectionDiffraction Efficiency: 0.88 (−0.53 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.95 (−0.21 dB) Mean Reflection DiffractionEfficiency: 0.92 (−0.37 dB)

TABLE 8-7 Light Beam LR2 Longest Wavelength (λ3U): 1560 nmPeriod/Wavelength (Λx/λ3U): 0.416 Direction angle φ: 0° Incidence Angleθ1: 52.5° Emergence Angle θ2: −56.2° P-Polarized Light ReflectionDiffraction Efficiency: 0.86 (−0.64 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.94 (−0.26 dB) Mean Reflection DiffractionEfficiency: 0.90 (−0.45 dB)

The comparison of Tables 7-1 to 7-7 with Tables 8-1 to 8-7 shows that,even when the direction angle φ equals 10°, it is possible to obtaindiffraction efficiency comparable with that obtained when the directionangle φ equals to 0°.

Now, a description will be given of the angle between the diffractedlight beam and the main period direction. Assuming that the anglebetween the principal ray of the diffracted light beam as projected onthe diffraction grating 52 and the main period direction is α, and thatthe wavelength is λ, it is necessary that the relationships expressed byformulae (J1) and (J2) be fulfilled. Moreover, where a relationshipclose to the Littrow arrangement is fulfilled as in this embodiment,formula (J3) holds.[n1·sin θ1−(λ/Λ)·cos φ]²+[(λ/Λ)·sin φ]²=(n1·sin θ2)²   (J1)sin α=λ·sin φ/(n1·Λ·sin θ2)   (J2)λ/Λ=2·n1·sin θ1   (J3)

From formulae (J1) to (J3), formula (J4) is obtained. Formula (J4) showsthat the diffracted light beam is apart from the main period directionby an angle twice the direction angle φ.sin α2·sin φ  (J4)

The diffraction grating 52 may be formed on a curved surface. In thatcase, as described earlier in connection with the ninth embodiment, at agiven point on the diffraction grating 52, the diffraction grating isprojected onto the plane P tangent thereto at that point, and theincidence angle θ1 with respect to the plane P and the period Λ asobserved on the plane P are so chosen as to fulfill the relationshipsexpressed by formulae (H1) to (H5).

In this embodiment, the diffraction grating receives two light beams LR1and LR2. It is, however, also possible to adopt a construction in whichthe diffraction grating receives three or more light beams in differentwavelength bands. In that case, the longest wavelength λ3U of thewavelength band in which, of all the received light beams, the onehaving the longest wavelength lies and the shortest wavelength λ2L ofthe wavelength band in which the one having the second longestwavelength lies are so chosen as to fulfill formula (H4).

Twelfth Embodiment

The optical apparatus 12 of a twelfth embodiment of the invention, too,is a transmitter/receiver apparatus for use in optical communication.This optical apparatus 12, like the optical apparatus 4 of the fourthembodiment shown in FIG. 6, transmits a light beam LT via an opticalfiber 31, and receives two light beams LR1 and LR2 via the optical fiber31. The light beams LT, LR1, and LR2 are in different wavelength bands.

Now, the design of the diffraction grating 52 formed on the diffractiongrating device 51 in the optical apparatus 12 will be described. Here,it is assumed that the main period of the elevations and depressions ofthe diffraction grating 52 is Λ; that the height difference between theelevations and depressions of the diffraction grating 52 is h; that, ofthe two media between which the diffraction grating 52 is sandwiched,the one present on the side thereof on which the light beam is incidenthas a refractive index of n1 and the other has a refractive index of n2;that the incidence angle at which the light beam is incident on thediffraction grating 52 is θ1; the emergence angle at which the lightbeam emerges from the diffraction grating 52 is θ2; that, of thewavelength bands in which the light beams LT, LR1, and LR2 lie, the onecovering the shortest wavelengths ranges from the shortest wavelength ofλ1L to the longest wavelength of λ1U, the one covering the longestwavelengths ranges from the shortest wavelength of λ3L to the longestwavelength of λ3U, and the one covering the middle wavelengths rangesfrom the shortest wavelength of λ2L to the longest wavelength of λ2U.

The diffraction grating 52 fulfills the relationships (K1) to (K5)below.λ1L<λ1U<λ2L<λ2U<λ3L<λ3U   (K1)n2<n1·sin θ1   (K2)1/(n1+n1·sin θ1)≦Λ/λ3U<Λ/λ2L≦1/(n2+n1·sin θ1)   (K3)1/(n2+n1·sin θ1)≦Λ/λ1U<Λ/λ1L≦2/(n1+n1·sin θ1)   (K4)Λ/λ3L<1/(2·n1·sin θ1)<Λ/λ2U   (K5)

Fulfilling these relationships, the diffraction grating 52 reflects(regularly reflects), by diffraction of the zero order, the transmittedlight beam LT, and reflects, by diffraction of the minus first order,the two received light beams LR1 and LR2.

FIG. 19 schematically shows the optical path observed in one practicalexample. In this example, the center wavelength of the received lightbeam LT is 1,310 nm, and the center wavelengths of the received lightbeams LR1 and LR2 are 1,490 nm and 1,555 nm, respectively; the lightbeams LT, LR1, and LR2 are made incident on the diffraction grating 52from inside the diffraction grating device 51. The relevant parametersare listed in Table 9-1. TABLE 9-1 Diffraction Grating 52 SectionalShape: Rectangular Elevation-Depression Period Λ: 0.645 μmElevation-Depression Height Difference h: 0.709 μm Elevation Width:0.451 μm Medium Refractive Index: 1.48 Light Beam LT Wavelength (λS):1310 nm Period/Wavelength (Λ/λS): 0.492 Incidence Angle θ1: 53°Emergence Angle θ2: 53° Reflectivity: 0.96 (−0.18 dB) Light Beam LR1Wavelength (λM): 1490 nm Period/Wavelength (Λ/λM): 0.433 Incidence Angleθ1: 53° Emergence Angle θ2: −49.7° P-Polarized Light ReflectionDiffraction Efficiency: 0.81 (−0.92 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.83 (−0.79 dB) Mean Reflection DiffractionEfficiency: 0.82 (−0.85 dB) P- And S-Polarized Light DiffractionEfficiency Difference: 0.13 dB Light Beam LR2 Wavelength (λL): 1555 nmPeriod/Wavelength (Λ/λL): 0.415 Incidence Angle θ1: 53° Emergence Angleθ2: −56.2° P-Polarized Light Reflection Diffraction Efficiency: 0.88(−0.56 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.90(−0.45 dB) Mean Reflection Diffraction Efficiency: 0.89 (−0.51 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.11 dB

In Table 9-1, the elevation width of the diffraction grating 52 denotesthe width of each of the parts thereof that are elevated toward the sideat which the light beams LT, LR1, and LR2 are incident (i.e., toward theinside of the diffraction grating device 51).

The parameters related to the shortest wavelength (λ1L) and the longestwavelength (λ1U) of the light beam LT as observed when the wavelengthband thereof has a width of 100 nm are listed in Tables 9-2 and 9-3. Theparameters related to the shortest wavelength (λ2L) and the longestwavelength (λ2U) of the light beam LR1 as observed when the wavelengthband thereof has a width of 20 nm are listed in Tables 9-4 and 9-5. Theparameters related to the shortest wavelength (λ3L) and the longestwavelength (λ3U) of the light beam LR2 as observed when the wavelengthband thereof has a width of 10 nm are listed in Tables 9-6 and 9-7.TABLE 9-2 Light Beam LT Shortest Wavelength (λ1L): 1260 nmPeriod/Wavelength (Λ/λ1L): 0.512 Incidence Angle θ1: 53° Emergence Angleθ2: 53° Reflectivity: 1.00 (−0.01 dB)

TABLE 9-3 Light Beam LT Longest Wavelength (λ1U): 1360 nmPeriod/Wavelength (Λ/λ1U): 0.474 Incidence Angle θ1: 53° Emergence Angleθ2: 53° Reflectivity: 0.89 (−0.49 dB)

TABLE 9-4 Light Beam LR1 Shortest Wavelength (λ2L): 1480 nmPeriod/Wavelength (Λ/λ2L): 0.436 Incidence Angle θ1: 53° Emergence Angleθ2: −48.8° P-Polarized Light Reflection Diffraction Efficiency: 0.76(−1.19 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.78(−1.09 dB) Mean Reflection Diffraction Efficiency: 0.77 (−1.14 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.10 dB

TABLE 9-5 Light Beam LR1 Longest Wavelength (λ2U): 1500 nmPeriod/Wavelength (Λ/λ2U): 0.430 Incidence Angle θ1: 53° Emergence Angleθ2: −50.7° P-Polarized Light Reflection Diffraction Efficiency: 0.85(−0.73 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.88(−0.58 dB) Mean Reflection Diffraction Efficiency: 0.86 (−0.65 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.15 dB

TABLE 9-6 Light Beam LR2 Shortest Wavelength (λ3L): 1550 nmPeriod/Wavelength (Λ/λ3L): 0.416 Incidence Angle θ1: 53° Emergence Angleθ2: −55.7° P-Polarized Light Reflection Diffraction Efficiency: 0.89(−0.52 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.91(−0.41 dB) Mean Reflection Diffraction Efficiency: 0.90 (−0.47 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.11 dB

TABLE 9-7 Light Beam LR2 Longest Wavelength (λ3U): 1560 nmPeriod/Wavelength (Λ/λ3U): 0.413 Incidence Angle θ1: 53° Emergence Angleθ2: −56.8° P-Polarized Light Reflection Diffraction Efficiency: 0.87(−0.60 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.89(−0.50 dB) Mean Reflection Diffraction Efficiency: 0.88 (−0.55 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.10 dB

The values of the lower and upper limits of formula (K3), i.e., thevalues of the following two formulae equal 0.376 and 0.458,respectively, and the values of the periods of the light beams LR1 andLR2 divided by the wavelengths thereof fulfill formula (K3).1/(n1+n1·sin θ1)1/(n2+n1·sin θ1)

Moreover, the values of the lower and upper limits of formula (K4),i.e., the values of the following two formulae equal 0.458 and 0.751,respectively, and the value of the period of the light beam LT dividedby the wavelength thereof fulfills formula (K4).1/(n2+n1·sin θ1)2/(n1+n1·sin θ1)

Furthermore, the value of the following formula is 0.423, and the valuesof the periods of the light beams LR1 and LR2 divided by the wavelengthsthereof fulfill formula (K5).1/(2·n1·sin θ1)

Fulfilling formula (K3) results in higher diffraction efficiency withthe light beams LR1 and LR2 having the longer wavelengths that arereflected by diffraction of the minus first order. Fulfilling formula(K4) results in higher diffraction efficiency with the light beam LThaving the shorter wavelength that is regularly reflected withoutdiffraction. Fulfilling formula (K5) results in smaller differencesbetween the diffraction efficiency with p-polarized light and that withs-polarized light in the light beams LR1 and LR2 having the longerwavelengths. With the design described above, the difference between thediffraction efficiency with p-polarized light and that with s-polarizedlight is 0.10 to 0.15 dB in the light beam LR1 and 0.10 to 0.11 dB inthe light beam LR2.

For comparison, the parameters as observed in a design that fulfillsformulae (K1) to (K4) but does not fulfill formula (K5) are listed inTables 10-1 to 10-7. TABLE 10-1 Diffraction Grating Sectional Shape:Rectangular Elevation-Depression Period Λ: 0.629 μm Elevation-DepressionHeight Difference h: 0.645 μm Elevation Width: 0.239 μm MediumRefractive Index: 1.5 Light Beam LT Wavelength (λS): 1310 nmPeriod/Wavelength (Λ/λS): 0.480 Incidence Angle θ1: 51° Emergence Angleθ2: 51° Reflectivity: 0.76 (−1.21 dB) Light Beam LR1 Wavelength (λM):1490 nm Period/Wavelength (Λ/λM): 0.422 Incidence Angle θ1: 51°Emergence Angle θ2: −53.3° P-Polarized Light Reflection DiffractionEfficiency: 0.95 (−0.22 dB) S-Polarized Light Reflection DiffractionEfficiency: 0.85 (−0.72 dB) Mean Reflection Diffraction Efficiency: 0.90(−0.46 dB) P- And S-Polarized Light Diffraction Efficiency Difference:0.51 dB Light Beam LR2 Wavelength (λL): 1555 nm Period/Wavelength(Λ/λL): 0.405 Incidence Angle θ1: 51° Emergence Angle θ2: −60.6°P-Polarized Light Reflection Diffraction Efficiency: 0.76 (−1.17 dB)S-Polarized Light Reflection Diffraction Efficiency: 0.75 (−1.23 dB)Mean Reflection Diffraction Efficiency: 0.76 (−1.20 dB) P- AndS-Polarized Light Diffraction Efficiency Difference: 0.06 dB

TABLE 10-2 Light Beam LT Shortest Wavelength (λ1L): 1260 nmPeriod/Wavelength (Λ/λ1L): 0.499 Incidence Angle θ1: 51° Emergence Angleθ2: 51° Reflectivity: 0.87 (−0.63 dB)

TABLE 10-3 Light Beam LT Longest Wavelength (λ1U): 1360 nmPeriod/Wavelength (Λ/λ1U): 0.463 Incidence Angle θ1: 51° Emergence Angleθ2: 51° Reflectivity: 0.74 (−1.32 dB)

TABLE 10-4 Light Beam LR1 Shortest Wavelength (λ2L): 1480 nmPeriod/Wavelength (Λ/λ2L): 0.425 Incidence Angle θ1: 51° Emergence Angleθ2: −52.3° P-Polarized Light Reflection Diffraction Efficiency: 0.96(−0.17 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.84(−0.76 dB) Mean Reflection Diffraction Efficiency: 0.90 (−0.45 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.59 dB

TABLE 10-5 Light Beam LR1 Longest Wavelength (λ2U): 1500 nmPeriod/Wavelength (Λ/λ2U): 0.419 Incidence Angle θ1: 51° Emergence Angleθ2: −54.4° P-Polarized Light Reflection Diffraction Efficiency: 0.93(−0.30 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.85(−0.73 dB) Mean Reflection Diffraction Efficiency: 0.89 (−0.51 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.43 dB

TABLE 10-6 Light Beam LR2 Shortest Wavelength (λ3L): 1550 nmPeriod/Wavelength (Λ/λ3L): 0.406 Incidence Angle θ1: 51° Emergence Angleθ2: −60.0° P-Polarized Light Reflection Diffraction Efficiency: 0.78(−1.06 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.77(−1.15 dB) Mean Reflection Diffraction Efficiency: 0.78 (−1.11 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.09 dB

TABLE 10-7 Light Beam LR2 Longest Wavelength (λ3U): 1560 nmPeriod/Wavelength (Λ/λ3U): 0.403 Incidence Angle θ1: 51° Emergence Angleθ2: −61.2° P-Polarized Light Reflection Diffraction Efficiency: 0.74(−1.28 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.74(−1.31 dB) Mean Reflection Diffraction Efficiency: 0.74 (−1.30 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.03 dB

With this design, the values of the lower and upper limits of formula(K3) are 0.375 and 0.462, respectively, and the values of the lower andupper limits of formula (K4) are 0.462 and 0.750, respectively. Thus,formulae (K3) and (K4) are fulfilled. On the other hand, the value of1/(2·n1·sin θ) is 0.429. Thus, formula (K5) is not fulfilled.

The difference between the diffraction efficiency with p-polarized lightand that with s-polarized light is as small as 0.03 to 0.09 in the lightbeam LR2 but as large as 0.43 to 0.59 in the light beam LR3.Consequently, the amount of light received by the light receiver 43 (seeFIG. 6) that receives the light beam LR2 greatly depends on thedirection of the polarization plane of the light beam LT3. Thus, topermit the light receiver 43 to receive a sufficiently large amount oflight, consideration needs to be given to the direction of thepolarization plane of the light beam LT3 anew from one optical apparatusto another. This makes it difficult to arrange the optical fiber 31relative to the diffraction grating device 51 and other components.

By contrast, in the optical apparatus 12 of this embodiment, of which anexample is listed in Tables 9-1 to 9-7, as described previously, thedifference between the diffraction efficiency with p-polarized light andthat with s-polarized light is small both in the light beams LR1 andLR2, and the amounts of light received by the light receivers 42 and 43do not greatly depend on the directions of the polarization planes ofthe light beams LR1 and LR2. Thus, it is possible to permit the lightreceivers 42 and 43 to receive sufficiently large amounts of light evenwith no consideration given to the directions of the polarization planesof the light beams LR1 and LR2.

The diffraction grating 52 may be formed on a curved surface. In thatcase, as described earlier in connection with the ninth embodiment, at agiven point on the diffraction grating 52, the diffraction grating isprojected onto the plane P tangent thereto at that point, and theincidence angle θ1 with respect to the plane P and the period Λ asobserved on the plane P are so chosen as to fulfill the relationshipsexpressed by formulae (K1) to (K5).

The diffraction efficiency observed when, in the practical examplelisted in Tables 9-1 to 9-7, the elevation width of the diffractiongrating 52 is varied by 0.05 μm is listed in Table 11. Table 11 lists,for each of the light beams LT, LR1, and LR2, the diffraction efficiencyobserved at whichever of the shortest, center, and longest wavelengthsyields the lowest diffraction efficiency. The values are all dBequivalent values. TABLE 11 Elevation Width Design Decrease ValueIncrease 0.401 μm 0.451 μm 0.501 μm Light Beam LT (1310 nm WavelengthBand) Reflectivity −1.337 −0.490 −0.095 Reflectivity Variation −0.8470.395 Light Beam LR1 (1490 nm Wavelength Band) Diffraction Efficiency−1.226 −1.136 −2.562 Diffraction Efficiency Variation −0.090 −1.425 P-And S-Polarized Light Diffraction 1.851 0.149 3.458 EfficiencyDifference P- And S-Polarized Light Diffraction 1.702 3.309 EfficiencyDifference Variation Light Beam LR2 (1555 nm Wavelength Band)Diffraction Efficiency −0.501 −0.552 −1.184 Diffraction EfficiencyVariation 0.051 −0.632 P- And S-Polarized Light Diffraction 0.558 0.1131.762 Efficiency Difference P- And S-Polarized Light Diffraction 0.4451.649 Efficiency Difference Variation

Table 11 shows that, when the elevation width varies from the designvalue, a great difference results between the diffraction efficiencywith p-polarized light and that with s-polarized light in the lightbeams LR1 and LR2 having the longer wavelengths. As will be describedbelow, however, this variation in the difference in diffractionefficiency resulting from a variation in the elevation width can bereduced.

Thirteenth Embodiment

The optical apparatus 13 of a thirteenth embodiment of the invention isa modified version of the optical apparatus 12 described above, themodification being such that, even when the elevation width of thediffraction grating 52 varies, no great difference results between thediffraction efficiency with p-polarized light and that with s-polarizedlight. In the optical apparatus 13, as in the optical apparatus 11 ofthe eleventh embodiment, as shown in FIG. 16, the elevations anddepressions of the diffraction grating 52 have separate periods in afirst and a second direction that are perpendicular to each other. Theperiod Λx in the first direction is smaller than the period Λy in thesecond direction, with the former referred to as the main period and thelatter as the sub period. The difference in the optical apparatus 13 isthat the light beams LT, LR1, and LR3 are made incident on thediffraction grating 52 from a direction perpendicular to the sub perioddirection. Thus, the direction angle φ shown in FIG. 17 is here 0°.

Also in this embodiment, the diffraction grating 52 fulfills therelationships expressed by formulae (K1) to (K5) noted earlier. Here,the main period Λx is substituted in A appearing in formulae (K3) to(K5).

The relevant parameters as observed in a design corresponding to thatlisted in Tables 9-1 to 9-7 are listed in Tables 12-1 to 12-7. Here, themain period Λx is assumed to be equal to the sub period Λy. The opticalpath of the light beams LT, LR1, and LR2 is the same as shown in FIG.19. TABLE 12-1 Diffraction Grating 52 Sectional Shape: RectangularElevation-Depression Main Period Λx (Λ): 0.645 μm Elevation-DepressionSub Period Λx: 0.645 μm Sub Period/Main Period (Λy/Λx): 1Elevation-Depression Height Difference h: 0.645 μm Main-Period-DirectionElevation Width Wx: 0.387 μm Sub-Period-Direction Elevation Width Wy:0.064 μm Medium Refractive Index: 1.48 Light Beam LT Wavelength (λS):1310 nm Period/Wavelength (Λx/λS): 0.492 Incidence Angle θ1: 53°Emergence Angle θ2: 53° Reflectivity: 0.84 (−0.77 dB) Light Beam LR1Wavelength (λM): 1490 nm Period/Wavelength (Λx/λM): 0.433 IncidenceAngle θ1: 53° Emergence Angle θ2: −49.7° P-Polarized Light ReflectionDiffraction Efficiency: 0.89 (−0.50 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.85 (−0.68 dB) Mean Reflection DiffractionEfficiency: 0.87 (−0.59 dB) P- And S-Polarized Light DiffractionEfficiency Difference: 0.18 dB Light Beam LR2 Wavelength (λL): 1555 nmPeriod/Wavelength (Λx/λL): 0.415 Incidence Angle θ1: 53° Emergence Angleθ2: −56.2° P-Polarized Light Reflection Diffraction Efficiency: 0.87(−0.62 dB) S-Polarized Light Reflection Diffraction Efficiency: 0.96(−0.20 dB) Mean Reflection Diffraction Efficiency: 0.91 (−0.40 dB) P-And S-Polarized Light Diffraction Efficiency Difference: 0.42 dB

TABLE 12-2 Light Beam LT Shortest Wavelength (λ1L): 1260 nmPeriod/Wavelength (Λx/λ1L): 0.512 Incidence Angle θ1: 53° EmergenceAngle θ2: 53° Reflectivity: 0.91 (−0.40 dB)

TABLE 12-3 Light Beam LT Longest Wavelength (λ1U): 1360 nmPeriod/Wavelength (Λx/λ1U): 0.474 Incidence Angle θ1: 53° EmergenceAngle θ2: 53° Reflectivity: 0.76 (−1.19 dB)

TABLE 12-4 Light Beam LR1 Shortest Wavelength (λ2L): 1480 nmPeriod/Wavelength (Λx/λ2L): 0.436 Incidence Angle θ1: 53° EmergenceAngle θ2: −48.8° P-Polarized Light Reflection Diffraction Efficiency:0.86 (−0.63 dB) S-Polarized Light Reflection Diffraction Efficiency:0.80 (−0.96 dB) Mean Reflection Diffraction Efficiency: 0.83 (−0.80 dB)P- And S-Polarized Light Diffraction Efficiency Difference: 0.33 dB

TABLE 12-5 Light Beam LR1 Longest Wavelength (λ2U): 1500 nmPeriod/Wavelength (Λx/λ2U): 0.430 Incidence Angle θ1: 53° EmergenceAngle θ2: −50.7° P-Polarized Light Reflection Diffraction Efficiency:0.91 (−0.42 dB) S-Polarized Light Reflection Diffraction Efficiency:0.90 (−0.47 dB) Mean Reflection Diffraction Efficiency: 0.90 (−0.45 dB)P- And S-Polarized Light Diffraction Efficiency Difference: 0.05 dB

TABLE 12-6 Light Beam LR2 Shortest Wavelength (λ3L): 1550 nmPeriod/Wavelength (Λx/λ3L): 0.416 Incidence Angle θ1: 53° EmergenceAngle θ2: −55.7° P-Polarized Light Reflection Diffraction Efficiency:0.88 (−0.56 dB) S-Polarized Light Reflection Diffraction Efficiency:0.96 (−0.17 dB) Mean Reflection Diffraction Efficiency: 0.92 (−0.36 dB)P- And S-Polarized Light Diffraction Efficiency Difference: 0.39 dB

TABLE 12-7 Light Beam LR2 Longest Wavelength (λ3U): 1560 nmPeriod/Wavelength (Λx/λ3U): 0.413 Incidence Angle θ1: 53° EmergenceAngle θ2: −56.8° P-Polarized Light Reflection Diffraction Efficiency:0.85 (−0.68 dB) S-Polarized Light Reflection Diffraction Efficiency:0.95 (−0.23 dB) Mean Reflection Diffraction Efficiency: 0.90 (−0.45 dB)P- And S-Polarized Light Diffraction Efficiency Difference: 0.45 dB

With this design, the values of the lower and upper limits of formula(K3) are 0.376 and 0.458, respectively, and the values of the lower andupper limits of formula (K4) are 0.458 and 0.751, respectively. Thus,formulae (K3) and (K4) are fulfilled. Moreover, the value of 1/(2·n1·sinθ) is 0.423. Thus, formula (K5), too, is fulfilled.

The diffraction efficiency observed when, in the practical examplelisted in Tables 12-1 to 12-7, the elevation width of the diffractiongrating 52 in the main and sub period directions is varied by 0.05 μm islisted in Tables 13-1 and 13-2. Tables 13-1 and 13-2 list, for each ofthe light beams LT, LR1, and LR2, the diffraction efficiency observed atwhichever of the shortest, center, and longest wavelengths yields thelowest diffraction efficiency. The values are all dB equivalent values.TABLE 13-1 Main-Period-Direction Elevation Width Design Decrease ValueIncrease   0.337 μm   0.387 μm   0.437 μm Light Beam LT (1310 nmWavelength Band) Reflectivity −1.608 −1.188 −0.589 ReflectivityVariation −0.419   0.599 Light Beam LR1 (1490 nm Wavelength Band)Diffraction Efficiency −0.724 −0.795 −1.071 Diffraction EfficiencyVariation   0.071 −0.276 P- And S-Polarized Light Diffraction   0.678  0.332   1.052 Efficiency Difference P- And S-Polarized LightDiffraction   0.346   0.720 Efficiency Difference Variation Light BeamLR2 (1555 nm Wavelength Band) Diffraction Efficiency −0.394 −0.448−0.663 Diffraction Efficiency Variation   0.054 −0.214 P- AndS-Polarized Light Diffraction   0.458   0.453   0.928 EfficiencyDifference P- And S-Polarized Light Diffraction   0.004   0.475Efficiency Difference Variation

TABLE 13-2 Sub-Period-Direction Elevation Width Design Decrease ValueIncrease   0.014 μm   0.064 μm   0.114 μm Light Beam LT (1310 nmWavelength Band) Reflectivity −1.556 −1.188 −0.806 ReflectivityVariation −0.367   0.383 Light Beam LR1 (1490 nm Wavelength Band)Diffraction Efficiency −0.757 −0.795 −0.937 Diffraction EfficiencyVariation   0.038 −0.142 P- And S-Polarized Light Diffraction   0.754  0.332   0.511 Efficiency Difference P- And S-Polarized LightDiffraction   0.422   0.179 Efficiency Difference Variation Light BeamLR2 (1555 nm Wavelength Band) Diffraction Efficiency −0.375 −0.448−0.580 Diffraction Efficiency Variation   0.073 −0.131 P- AndS-Polarized Light Diffraction   0.256   0.453   0.768 EfficiencyDifference P- And S-Polarized Light Diffraction −0.198   0.314Efficiency Difference Variation

It will be understood that, whereas the variation of the elevation widthof the diffraction grating 52 is the same between in Table 11 and Tables13-1 and 13-2 (i.e., ±0.05 μm), the increase in the difference betweenthe diffraction efficiency with p-polarized light and that withs-polarized light in the light beams LR1 and LR2 having the longerwavelengths is minimized in this embodiment.

Now, a description will be given of the relationship between the subperiod Λy of the diffraction grating 52 and the diffracted light. Letthe wavelength of light be λ, the order of the diffraction produced bythe main period Λx be mx, and the order of the diffraction produced bythe sub period Λy be my. Then, the condition under which diffractedlight of orders (mx, my) is produced is expressed by formula (M1).$\begin{matrix}{{\left\lbrack {{{\left( {n\quad{2/n}\quad 1} \right) \cdot \sin}\quad\theta\quad{1 \cdot \cos}\quad\varphi} + {{mx} \cdot {\lambda/\left( {n\quad{2 \cdot \Lambda}\quad x} \right)}}} \right\rbrack^{2} + \left\lbrack {{{\left( {n\quad{2/n}\quad 1} \right) \cdot \sin}\quad\theta\quad{1 \cdot \cos}\quad\varphi} + {{my} \cdot {\lambda/\left( {n\quad{2 \cdot {\Lambda y}}} \right)}}} \right\rbrack^{2}} \leq 1} & \left( {M\quad 1} \right)\end{matrix}$

In the optical apparatus 13, diffraction of orders (−1, 0), i.e., withmx=−1 and my=0, needs to be produced in the light beams LR1 and LR2 withhigh diffraction efficiency. To achieve this, diffraction of otherorders needs to be reduced. Here, of all the diffracted light of otherorders than orders (−1, 0), the most likely to be produced is that oforders (−1, +1), i.e., with mx=−1 and my=±1. The condition under whichno diffracted light of orders (−1, +1) is produced in the light beamsLR1 and LR2 is expressed by formula (M2).[sin θ1−λ2L/(n1Λx)]²+{λ2L/(n 1·Λy)}²>1   (M2)

Formula (M2) can be rearranged to obtain formula (M3).Λy ²/λ2L ²<1/{n1²·[1−(sin θ1−λ2L/(n 1·Λx))²]}  (M3)

Here, fulfilling formula (M4) suffices to reduce the diffracted light oforders (−1, ±1) produced in the light beams LR1 and LR2.Λy ²/λ2L ²<1/{n1²·[1−(sin θ1−1.1·λ2L/(n1·Λx))²]}  (M4)

For easy production of the diffraction grating 52, it is preferable thatthe sub period Ay be greater than the main period Λx; specifically, itis preferable that formula (M5) be fulfilled.Λx ²/λ2L ² ≦Λy ²/λ2L ²   (M5)

The relevant parameters observed in a design in which, in addition toformulae (K1) to (K5), formulae (M4) and (M5) are fulfilled are listedin Tables 14-1 to 14-7. Here, the sub period Λy is twice the main periodΛx. TABLE 14-1 Diffraction Grating 52 Sectional Shape: RectangularElevation-Depression Main Period Λx (Λ): 0.649 μm Elevation-DepressionSub Period Λx: 1.298 μm Sub Period/Main Period (Λy/Λx): 2Elevation-Depression Height Difference h: 0.649 μm Main-Period-DirectionElevation Width Wx: 0.389 μm Sub-Period-Direction Elevation Width Wy:0.130 μm Medium Refractive Index: 1.48 Light Beam LT Wavelength (λS):1310 nm Period/Wavelength (Λx/λS): 0.495 Incidence Angle θ1: 52.5°Emergence Angle θ2: 52.5° Reflectivity: 0.81 (−0.90 dB) Light Beam LR1Wavelength (λM): 1490 nm Period/Wavelength (Λx/λM): 0.436 IncidenceAngle θ1: 52.5° Emergence Angle θ2: −49.3° P-Polarized Light ReflectionDiffraction Efficiency: 0.88 (−0.55 dB) S-Polarized Light ReflectionDiffraction Efficiency: 0.85 (−0.71 dB) Mean Reflection DiffractionEfficiency: 0.86 (−0.63 dB) P- And S-Polarized Light DiffractionEfficiency Difference: 0.16 dB Light Beam LR2 Wavelength (λL): 1555 nmPeriod/Wavelength (Λx/λL): 0.417 Incidence Angle θ1: 52.5° EmergenceAngle θ2: −55.7° P-Polarized Light Reflection Diffraction Efficiency:0.87 (−0.59 dB) S-Polarized Light Reflection Diffraction Efficiency:0.95 (−0.23 dB) Mean Reflection Diffraction Efficiency: 0.91 (−0.41 dB)P- And S-Polarized Light Diffraction Efficiency Difference: 0.35 dB

TABLE 14-2 Light Beam LT Shortest Wavelength (λ1L): 1260 nmPeriod/Wavelength (Λx/λ1L): 0.515 Incidence Angle θ1: 52.5° EmergenceAngle θ2: 52.5° Reflectivity: 0.88 (−0.57 dB)

TABLE 14-3 Light Beam LT Longest Wavelength (λ1U): 1360 nmPeriod/Wavelength (Λx/λ1U): 0.477 Incidence Angle θ1: 52.5° EmergenceAngle θ2: 52.5° Reflectivity: 0.76 (−1.21 dB)

TABLE 14-4 Light Beam LR1 Shortest Wavelength (λ2L): 1480 nmPeriod/Wavelength (Λx/λ2L): 0.438 Incidence Angle θ1: 52.5° EmergenceAngle θ2: −48.4° P-Polarized Light Reflection Diffraction Efficiency:0.85 (−0.70 dB) S-Polarized Light Reflection Diffraction Efficiency:0.79 (−1.00 dB) Mean Reflection Diffraction Efficiency: 0.82 (−0.85 dB)P- And S-Polarized Light Diffraction Efficiency Difference: 0.30 dB

TABLE 14-5 Light Beam LR1 Longest Wavelength (λ2U): 1500 nmPeriod/Wavelength (Λx/λ2U): 0.433 Incidence Angle θ1: 52.5° EmergenceAngle θ2: −50.2° P-Polarized Light Reflection Diffraction Efficiency:0.90 (−0.45 dB) S-Polarized Light Reflection Diffraction Efficiency:0.89 (−0.50 dB) Mean Reflection Diffraction Efficiency: 0.90 (−0.48 dB)P- And S-Polarized Light Diffraction Efficiency Difference: 0.05 dB

TABLE 14-6 Light Beam LR2 Shortest Wavelength (λ3L): 1550 nmPeriod/Wavelength (Λx/λ3L): 0.419 Incidence Angle θ1: 52.5° EmergenceAngle θ2: −55.1° P-Polarized Light Reflection Diffraction Efficiency:0.88 (−0.53 dB) S-Polarized Light Reflection Diffraction Efficiency:0.95 (−0.21 dB) Mean Reflection Diffraction Efficiency: 0.92 (−0.37 dB)P- And S-Polarized Light Diffraction Efficiency Difference: 0.33 dB

TABLE 14-7 Light Beam LR2 Longest Wavelength (λ3U): 1560 nmPeriod/Wavelength (Λx/λ3U): 0.416 Incidence Angle θ1: 52.5° EmergenceAngle θ2: −56.2° P-Polarized Light Reflection Diffraction Efficiency:0.86 (−0.64 dB) S-Polarized Light Reflection Diffraction Efficiency:0.94 (−0.26 dB) Mean Reflection Diffraction Efficiency: 0.90 (−0.45 dB)P- And S-Polarized Light Diffraction Efficiency Difference: 0.38 dB

With this design, the values of the lower and upper limits of formula(K3) are 0.377 and 0.460, respectively, and the values of the lower andupper limits of formula (K4) are 0.460 and 0.754, respectively.Moreover, the value of 1/(2·n1·sin θ1) appearing in formula (K5) is0.426. The sub period Ay, which corresponds to the upper limit value offormula (M3), is 1.338 μm.

The diffraction efficiency observed when, in the practical examplelisted in Tables 14-1 to 14-7, the elevation width of the diffractiongrating 52 in the main and sub period directions is varied by 0.05 μm islisted in Tables 15-1 and 15-2. Tables 15-1 and 15-2 list, for each ofthe light beams LT, LR1, and LR2, the diffraction efficiency observed atwhichever of the shortest, center, and longest wavelengths yields thelowest diffraction efficiency. The values are all dB equivalent values.TABLE 15-1 Main-Period-Direction Elevation Width Design Decrease ValueIncrease 0.339 μm 0.389 μm 0.439 μm Light Beam LT (1310 nm WavelengthBand) Reflectivity −1.685 −1.208 −0.597 Reflectivity Variation −0.4770.611 Light Beam LR1 (1490 nm Wavelength Band) Diffraction Efficiency−0.796 −0.848 −1.125 Diffraction Efficiency Variation 0.052 −0.276 P-And S-Polarized Light Diffraction 0.808 0.300 1.155 EfficiencyDifference P- And S-Polarized Light Diffraction 0.508 0.855 EfficiencyDifference Variation Light Beam LR2 (1555 nm Wavelength Band)Diffraction Efficiency −0.370 −0.449 −0.649 Diffraction EfficiencyVariation 0.079 −0.200 P- And S-Polarized Light Diffraction 0.340 0.3820.898 Efficiency Difference P- And S-Polarized Light Diffraction −0.0420.515 Efficiency Difference Variation

TABLE 15-2 Sub-Period-Direction Elevation Width Design Decrease ValueIncrease 0.080 μm 0.130 μm 0.180 μm Light Beam LT (1310 nm WavelengthBand) Reflectivity −1.388 −1.208 −1.103 Reflectivity Variation −0.1800.105 Light Beam LR1 (1490 nm Wavelength Band) Diffraction Efficiency−0.803 −0.848 −0.933 Diffraction Efficiency Variation 0.045 −0.085 P-And S-Polarized Light Diffraction 0.808 0.300 0.327 EfficiencyDifference P- And S-Polarized Light Diffraction 0.508 0.027 EfficiencyDifference Variation Light Beam LR2 (1555 nm Wavelength Band)Diffraction Efficiency −0.370 −0.449 −0.522 Diffraction EfficiencyVariation 0.079 −0.073 P- And S-Polarized Light Diffraction 0.340 0.3820.579 Efficiency Difference P- And S-Polarized Light Diffraction −0.0420.197 Efficiency Difference Variation

The comparison of Tables 13-1 and 13-2 with Tables 15-1 and 15-2 showsthat, by making the sub period Λy greater than the main period Λx, it ispossible to more effectively minimize the increase in the differencebetween the diffraction efficiency with p-polarized light and that withs-polarized light in the light beams LR1 and LR2 resulting from avariation in the elevation width.

Obviously, many modifications and variations of the present inventionare possible in light of the above teachings. It is therefore to beunderstood that within the scope of the appended claims, the inventionmay be practiced other than as specifically described.

1. A diffraction grating device on which a first light beam having afirst wavelength and a second light beam having a second wavelengthlonger than the first wavelength are made incident from differentdirections, the diffraction grating device making the first light beamemerge therefrom in the direction from which the second light beam isincident, wherein the following relationships are fulfilled:n2≧n1·sin θ;Λ/λL≦1/(n1+n1·sin θ); andΛ/λS>1/(n1+n1·sin θ)−0.04, where n1 represents a refractive index of afirst medium present on a side of a diffraction grating on which thefirst light beam is incident; n2 represents a refractive index of asecond medium present on a side of the diffraction grating opposite tothe side thereof on which the first light beam is incident; Λ representsa period of elevations and depressions on the diffraction grating; λSrepresents the wavelength of the first light beam; λL represents thewavelength of the second light beam; and θ represents an incidence angleat which the first light beam is incident on the diffraction grating. 2.A diffraction grating device on which a first light beam having a firstwavelength and a second light beam having a second wavelength longerthan the first wavelength are made incident from different directions,the diffraction grating device making the first light beam emergetherefrom in the direction from which the second light beam is incident,wherein the following relationships are fulfilled:n2<n1·sin θ;Λ/λL≦1/(n1+n1·sin θ); and1/(n1+n1·sin θ)≦Λ/λS≦1/(n2+n1·sin θ), where n1 represents a refractiveindex of a first medium present on a side of a diffraction grating onwhich the first light beam is incident; n2 represents a refractive indexof a second medium present on a side of the diffraction grating oppositeto the side thereof on which the first light beam is incident; Λrepresents a period of elevations and depressions on the diffractiongrating; λS represents the wavelength of the first light beam; λLrepresents the wavelength of the second light beam; and θ represents anincidence angle at which the first light beam is incident on thediffraction grating.
 3. A diffraction grating device on which a firstlight beam having a first wavelength and a second light beam having asecond wavelength longer than the first wavelength are made incidentfrom different directions, the diffraction grating device making thefirst light beam emerge therefrom in the direction from which the secondlight beam is incident, wherein the following relationships arefulfilled:n2<n1·sin θ;1/(n1+n1·sin θ)≦Λ/λL≦1/(n2+n1·sin θ); and1/(n2+n1·sin θ)≦Λ/λS≦2/(n1+n1·sin θ), where n1 represents a refractiveindex of a first medium present on a side of a diffraction grating onwhich the first light beam is incident; n2 represents a refractive indexof a second medium present on a side of the diffraction grating oppositeto the side thereof on which the first light beam is incident; Λrepresents a period of elevations and depressions on the diffractiongrating; λS represents the wavelength of the first light beam; λLrepresents the wavelength of the second light beam; and θ represents anincidence angle at which the first light beam is incident on thediffraction grating.
 4. A diffraction grating device on which a firstlight beam having a first wavelength and a second light beam having asecond wavelength longer than the first wavelength are made incidentfrom different directions, the diffraction grating device making thefirst light beam emerge therefrom in the direction from which the secondlight beam is incident, wherein the following relationships arefulfilled:n2≧n1·sin θ;Λ/λL≦1/(n2+n1·sin θ); and1/(n2+n1·sin θ)−0.04<Λ/λS<1/(n2+n1·sin θ)+0.02, where n1 represents arefractive index of a first medium present on a side of a diffractiongrating on which the first light beam is incident; n2 represents arefractive index of a second medium present on a side of the diffractiongrating opposite to the side thereof on which the first light beam isincident; Λ represents a period of elevations and depressions on thediffraction grating; λS represents the wavelength of the first lightbeam; λL represents the wavelength of the second light beam; and θrepresents an incidence angle at which the first light beam is incidenton the diffraction grating.
 5. The diffraction grating device of claim1, wherein the diffraction grating device has, separate from a surfaceon which the diffraction grating is formed, a surface capable ofcondensing light.
 6. The diffraction grating device of claim 2, whereinthe diffraction grating device has, separate from a surface on which thediffraction grating is formed, a surface capable of condensing light. 7.The diffraction grating device of claim 3, wherein the diffractiongrating device has, separate from a surface on which the diffractiongrating is formed, a surface capable of condensing light.
 8. Thediffraction grating device of claim 4, wherein the diffraction gratingdevice has, separate from a surface on which the diffraction grating isformed, a surface capable of condensing light.
 9. The diffractiongrating device of claim 1, wherein the diffraction grating is formed ona curved surface.
 10. The diffraction grating device of claim 2, whereinthe diffraction grating is formed on a curved surface.
 11. Thediffraction grating device of claim 3, wherein the diffraction gratingis formed on a curved surface.
 12. The diffraction grating device ofclaim 4, wherein the diffraction grating is formed on a curved surface.13. An optical apparatus that splits or couples a plurality of lightbeams having different wavelengths, wherein the optical apparatuscomprises the diffraction grating device of claim 1, and uses thediffraction grating to split or couple the light beams.
 14. An opticalapparatus that splits or couples a plurality of light beams havingdifferent wavelengths, wherein the optical apparatus comprises thediffraction grating device of claim 2, and uses the diffraction gratingto split or couple the light beams.
 15. An optical apparatus that splitsor couples a plurality of light beams having different wavelengths,wherein the optical apparatus comprises the diffraction grating deviceof claim 3, and uses the diffraction grating to split or couple thelight beams.
 16. An optical apparatus that splits or couples a pluralityof light beams having different wavelengths, wherein the opticalapparatus comprises the diffraction grating device of claim 4, and usesthe diffraction grating to split or couple the light beams.
 17. Theoptical apparatus of claim 13, wherein the optical apparatus furthercomprises a mechanism for varying an incidence angle at which a lightbeam is incident on the diffraction grating.
 18. The optical apparatusof claim 14, wherein the optical apparatus further comprises a mechanismfor varying an incidence angle at which a light beam is incident on thediffraction grating.
 19. The optical apparatus of claim 15, wherein theoptical apparatus further comprises a mechanism for varying an incidenceangle at which a light beam is incident on the diffraction grating. 20.The optical apparatus of claim 16, wherein the optical apparatus furthercomprises a mechanism for varying an incidence angle at which a lightbeam is incident on the diffraction grating.
 21. A diffraction gratingdevice that diffracts and reflects a light beam in a first band ofwavelengths and that diffracts and reflects and thereby separates aplurality of light beams in a plurality of bands of wavelengths longerthan the wavelengths of the first band, the plurality of light beamsbeing incident from a direction in which the light beam in the firstband of wavelengths is diffracted, wherein elevations and depressions ona diffraction grating have a first period in a first direction and asecond period longer than the first period in a second directionperpendicular to the first direction, and wherein the followingrelationships are fulfilled:λ1L<λ1U<λ2L<λ2U<λ3L<λ3U;n2<n1·sin θ;φ≠0;1/[n  1 ⋅ (1 − sin²θ ⋅ sin²φ)^(1/2) + n  1 ⋅ sin   θ ⋅ cos   φ] ≤ Λ/λ  3U < Λ/λ  2L ≤ 1/[(n  2² − n  1² ⋅ sin²θ ⋅ sin²φ)^(1/2) + n  1 ⋅ sin   θ ⋅ cos   φ]; and1/[(n  2² − n  1² ⋅ sin²θ ⋅ sin²φ)^(1/2) + n  1 ⋅ sin   θ ⋅ cos   φ] ≤ Λ/λ  1U < Λ/λ  1L ≤ 2/[n  1 ⋅ (1 − sin²θ ⋅ sin²φ)^(1/2) + n  1 ⋅ sin   θ ⋅ cos   φ],where n1 represents a refractive index of a first medium present on aside of the diffraction grating that faces optical paths of the lightbeams; n2 represents a refractive index of a second medium present on aside of the diffraction grating opposite to the side thereof facing theoptical paths of the light beams; θ represents an incidence angle atwhich a principal ray of the light beams is incident on the diffractiongrating; φ represents an angle between a plane perpendicular to thediffraction grating and parallel to the first direction and an incidenceplane of the principal ray of the light beams; Λ represents the firstperiod of the elevations and depressions on the diffraction grating; λ1Lrepresents a shortest wavelength of the first band of wavelengths; λ1Urepresents a longest wavelength of the first band of wavelengths; λ2Lrepresents a shortest wavelength of, of the plurality of bands ofwavelengths longer than the wavelengths of the first band, a band ofshortest wavelengths; λ2U represents a longest wavelength of, of theplurality of bands of wavelengths longer than the wavelengths of thefirst band, a band of shortest wavelengths; λ3L represents a shortestwavelength of, of the plurality of bands of wavelengths longer than thewavelengths of the first band, a band of longest wavelengths; and λ3Urepresents a longest wavelength of, of the plurality of bands ofwavelengths longer than the wavelengths of the first band, a band oflongest wavelengths.
 22. A diffraction grating device that separates aplurality of light beams spread in different wavelength bands andoverlapping with one another, wherein elevations and depressions of adiffraction grating have a first period in a first direction and asecond period longer than the first period in a second directionperpendicular to the first direction, wherein the diffraction gratingdiffracts and reflects a light beam incident thereon in a same directionfrom which the light beam is incident with respect to a normal to thediffraction grating at a position at which the light beam is incident,and wherein an angle between a plane perpendicular to the diffractiongrating and parallel to the first direction and an incidence plane of aprincipal ray of the light beam incident on the diffraction grating is0.5° or more but 15° or less.
 23. An optical apparatus comprising afirst optical component that supplies a light beam in a first band ofwavelengths and a second optical component that supplies a plurality oflight beams in different bands of wavelengths longer than thewavelengths of the first band and that receives the light beam in thefirst band of wavelengths from the first optical component, wherein theoptical apparatus comprises the diffraction grating device of claim 21,and uses the diffraction grating to diffract and reflect and therebydirect the light beam from the first optical component to the secondoptical component and to diffract and reflect and thereby separate theplurality of light beams from the second optical component.
 24. Theoptical apparatus of claim 23, wherein the second optical component isan optical fiber.
 25. The optical apparatus of claim 23, wherein theoptical apparatus further comprises an optical component that condensesa light beam incident on or emerging from the diffraction grating. 26.An optical apparatus comprising an optical component that supplies aplurality of light beams spread in different wavelength bands andoverlapping with one another, the optical apparatus separating theplurality of light beams, wherein the optical apparatus comprises thediffraction grating device of claim 22, and uses the diffraction gratingto separate the plurality of light beams.
 27. The optical apparatus ofclaim 26, wherein the component that supplies the plurality of lightbeams is an optical fiber.
 28. The optical apparatus of claim 26,wherein the optical apparatus further comprises an optical componentthat condenses a light beam incident on or emerging from the diffractiongrating.
 29. A diffraction grating device that diffracts and reflects alight beam in a first band of wavelengths and that diffracts andreflects and thereby separates a plurality of light beams in a pluralityof bands of wavelengths longer than the wavelengths of the first band,the plurality of light beams being incident from a direction in whichthe light beam in the first band of wavelengths is diffracted, whereinthe following relationships are fulfilled:λ1L<λ1U<λ2L<λ2U<λ3L<λ3U;n2<n1·sin θ;1/(n1+n1·sin θ)≦Λ/λ3U<Λ/λ2L≦1/(n2+n1·sin θ);1/(n2+n1·sin θ)≦Λ/λ1U<Λ/λ1L≦2/(n1+n1·sin θ); andΛ/λ3L<1/(2·n1·sin θ)<Λ/λ2U, where n1 represents a refractive index of afirst medium present on a side of the diffraction grating that facesoptical paths; n2 represents a refractive index of a second mediumpresent on a side of the diffraction grating opposite to the sidethereof facing the optical paths; θ represents an incidence angle atwhich a principal ray of the light beams is incident on the diffractiongrating; Λ represents a period of the elevations and depressions on thediffraction grating; λ1L represents a shortest wavelength of the firstband of wavelengths; λ1U represents a longest wavelength of the firstband of wavelengths; λ2L represents a shortest wavelength of, of theplurality of bands of wavelengths longer than the wavelengths of thefirst band, a band of shortest wavelengths; λ2U represents a longestwavelength of, of the plurality of bands of wavelengths longer than thewavelengths of the first band, a band of shortest wavelengths; λ3Lrepresents a shortest wavelength of, of the plurality of bands ofwavelengths longer than the wavelengths of the first band, a band oflongest wavelengths; and λ3U represents a longest wavelength of, of theplurality of bands of wavelengths longer than the wavelengths of thefirst band, a band of longest wavelengths.
 30. The diffraction gratingdevice of claim 29, wherein the period is a period that the elevationsand depressions on the diffraction grating have in a first directionsubstantially parallel to an incidence plane of a principal ray of theincident light beams, and the elevations and depressions on thediffraction grating have another period in a second directionperpendicular to the first direction.
 31. The diffraction grating deviceof claim 30, wherein the following relationship is fulfilled:Λ²/λ2L ² ≦Λy ²/λ2L ²<1/{n1²·[1−(sin θ−1.1·λ2L/(n1·Λ))²]} where Λyrepresents the period of the elevations and depressions on thediffraction grating in the second direction.
 32. An optical apparatuscomprising a first optical component that supplies a light beam in afirst band of wavelengths and a second optical component that supplies aplurality of light beams in different bands of wavelengths longer thanthe wavelengths of the first band and that receives the light beam inthe first band of wavelengths from the first optical component, whereinthe optical apparatus comprises the diffraction grating device of claim29, and uses the diffraction grating to diffract and reflect and therebydirect the light beam from the first optical component to the secondoptical component and to diffract and reflect and thereby separate theplurality of light beams from the second optical component.
 33. Theoptical apparatus of claim 32, wherein the second optical component isan optical fiber.
 34. The optical apparatus of claim 32, wherein theoptical apparatus further comprises an optical component that condensesa light beam incident on or emerging from the diffraction grating.